Daily Papers

Masked image modeling has become a dominant paradigm for SAR pre-training, yet the design of the reconstruction target remains fundamentally unsettled. This article argues that a SAR pre-training target should satisfy two conditions to produce transferable representations: (i) physics-grounded stability, i.e., approximate invariance of the target operator to multiplicative speckle inherent in coherent imaging; and (ii) semantic scale compatibility, i.e., coverage of the heterogeneous spatial scales that downstream tasks demand. These two conditions are individually achievable but jointly difficult: physics-grounded stability favors fixed operators, while semantic scale compatibility favors data-driven composition. To this end, SARATR-X-v2 reconciles both within a single design. The target is constructed through fixed structural extractors spanning six receptive fields, from blind-spot local aggregation to directional log-ratio region contrast, and fused via learnable weights into one unified supervision signal for masked reconstruction. On twelve SAR benchmarks across classification, detection, and segmentation, SARATR-X-v2 achieves state-of-the-art transfer performance. Under synthetic speckle variation, the proposed target reduces perturbation drift in the learned supervision by nearly two orders of magnitude relative to pixel-space supervision. Taken together, these results support physics-grounded stability and semantic scale compatibility as a principled framework for pre-training target design under coherent imaging, and suggest that effective SAR pre-training is not about reconstructing more signal, but about reconstructing the right structural target.

Multiplicative noise, also known as speckle or pepper noise, commonly affects images produced by synthetic aperture radar (SAR), lasers, or optical lenses. Unlike additive noise, which typically arises from thermal processes or external factors, multiplicative noise is inherent to the system, originating from the fluctuation in diffuse reflections. These fluctuations result in multiple copies of the same signal with varying magnitudes being combined. Consequently, despeckling, or removing multiplicative noise, necessitates different techniques compared to those used for additive noise removal. In this paper, we propose a novel approach using Stochastic Differential Equations based diffusion models to address multiplicative noise. We demonstrate that multiplicative noise can be effectively modeled as a Geometric Brownian Motion process in the logarithmic domain. Utilizing the Fokker-Planck equation, we derive the corresponding reverse process for image denoising. To validate our method, we conduct extensive experiments on two different datasets, comparing our approach to both classical signal processing techniques and contemporary CNN-based noise removal models. Our results indicate that the proposed method significantly outperforms existing methods on perception-based metrics such as FID and LPIPS, while maintaining competitive performance on traditional metrics like PSNR and SSIM.

Speckle is a multiplicative noise which affects all coherent imaging modalities including Synthetic Aperture Radar (SAR) images. The presence of speckle degrades the image quality and adversely affects the performance of SAR image understanding applications such as automatic target recognition and change detection. Thus, SAR despeckling is an important problem in remote sensing. In this paper, we introduce SAR-DDPM, a denoising diffusion probabilistic model for SAR despeckling. The proposed method comprises of a Markov chain that transforms clean images to white Gaussian noise by repeatedly adding random noise. The despeckled image is recovered by a reverse process which iteratively predicts the added noise using a noise predictor which is conditioned on the speckled image. In addition, we propose a new inference strategy based on cycle spinning to improve the despeckling performance. Our experiments on both synthetic and real SAR images demonstrate that the proposed method achieves significant improvements in both quantitative and qualitative results over the state-of-the-art despeckling methods.

Speckle fluctuations seriously limit the interpretability of synthetic aperture radar (SAR) images. Speckle reduction has thus been the subject of numerous works spanning at least four decades. Techniques based on deep neural networks have recently achieved a new level of performance in terms of SAR image restoration quality. Beyond the design of suitable network architectures or the selection of adequate loss functions, the construction of training sets is of uttermost importance. So far, most approaches have considered a supervised training strategy: the networks are trained to produce outputs as close as possible to speckle-free reference images. Speckle-free images are generally not available, which requires resorting to natural or optical images or the selection of stable areas in long time series to circumvent the lack of ground truth. Self-supervision, on the other hand, avoids the use of speckle-free images. We introduce a self-supervised strategy based on the separation of the real and imaginary parts of single-look complex SAR images, called MERLIN (coMplex sElf-supeRvised despeckLINg), and show that it offers a straightforward way to train all kinds of deep despeckling networks. Networks trained with MERLIN take into account the spatial correlations due to the SAR transfer function specific to a given sensor and imaging mode. By requiring only a single image, and possibly exploiting large archives, MERLIN opens the door to hassle-free as well as large-scale training of despeckling networks. The code of the trained models is made freely available at https://gitlab.telecom-paris.fr/RING/MERLIN.

Multi-Resolution Hash Encoding (MHE), the foundational technique behind Instant Neural Graphics Primitives, provides a powerful parameterization for neural fields. However, its spatial behavior lacks rigorous understanding from a physical systems perspective, leading to reliance on heuristics for hyperparameter selection. This work introduces a novel analytical approach that characterizes MHE by examining its Point Spread Function (PSF), which is analogous to the Green's function of the system. This methodology enables a quantification of the encoding's spatial resolution and fidelity. We derive a closed-form approximation for the collision-free PSF, uncovering inherent grid-induced anisotropy and a logarithmic spatial profile. We establish that the idealized spatial bandwidth, specifically the Full Width at Half Maximum (FWHM), is determined by the average resolution, N_{avg}. This leads to a counterintuitive finding: the effective resolution of the model is governed by the broadened empirical FWHM (and therefore N_{avg}), rather than the finest resolution N_{max}, a broadening effect we demonstrate arises from optimization dynamics. Furthermore, we analyze the impact of finite hash capacity, demonstrating how collisions introduce speckle noise and degrade the Signal-to-Noise Ratio (SNR). Leveraging these theoretical insights, we propose Rotated MHE (R-MHE), an architecture that applies distinct rotations to the input coordinates at each resolution level. R-MHE mitigates anisotropy while maintaining the efficiency and parameter count of the original MHE. This study establishes a methodology based on physical principles that moves beyond heuristics to characterize and optimize MHE.

The Pleiades is the most prominent open star cluster visible from Earth and an important benchmark for simple stellar populations, unified by common origin, age, and distance. Binary stars are its essential ingredient, yet their contribution remains uncertain due to heavy observational biases. A resolved multiplicity survey was conducted for a magnitude-limited G < 15mag sample of 423 potential cluster members, including sources with poorly fitted astrometric solutions in Gaia DR3. Speckle interferometric observations at the 2.5 meter telescope of SAI MSU observatory were combined with Gaia data, enabling the identification of 61 resolved binary or multiple systems within the 0.04 - 10 arcsec (5 - 1350 au) separation range. With speckle observations, we discovered 21 components in 20 systems. The existence of a Merope (23 Tau) companion is confirmed after several previous unsuccessful attempts. We show that the Gaia multipeak fraction is a strong predictor of subarcsecond multiplicity, as all sources with ipd_frac_multi_peak > 4% are successfully resolved. We found that 10% of Pleiades stars have a companion with a mass ratio q > 0.5 within projected separation of 27 < s < 1350 au, and confirm a deficit of wide binaries with s > 300 au. An observed dearth of wide pairs with large mass ratio (q > 0.55) may imprint the transition from hard to soft binaries regime at the early stages of cluster evolution. The total binary fraction for q > 0.5 systems is extrapolated to be around 25%.

We introduce a general framework for generating diverse visual content, including ambiguous images, panorama images, mesh textures, and Gaussian splat textures, by synchronizing multiple diffusion processes. We present exhaustive investigation into all possible scenarios for synchronizing multiple diffusion processes through a canonical space and analyze their characteristics across applications. In doing so, we reveal a previously unexplored case: averaging the outputs of Tweedie's formula while conducting denoising in multiple instance spaces. This case also provides the best quality with the widest applicability to downstream tasks. We name this case SyncTweedies. In our experiments generating visual content aforementioned, we demonstrate the superior quality of generation by SyncTweedies compared to other synchronization methods, optimization-based and iterative-update-based methods.

We develop a multiexposure image fusion method based on texture features, which exploits the edge preserving and intraregion smoothing property of nonlinear diffusion filters based on partial differential equations (PDE). With the captured multiexposure image series, we first decompose images into base layers and detail layers to extract sharp details and fine details, respectively. The magnitude of the gradient of the image intensity is utilized to encourage smoothness at homogeneous regions in preference to inhomogeneous regions. Then, we have considered texture features of the base layer to generate a mask (i.e., decision mask) that guides the fusion of base layers in multiresolution fashion. Finally, well-exposed fused image is obtained that combines fused base layer and the detail layers at each scale across all the input exposures. Proposed algorithm skipping complex High Dynamic Range Image (HDRI) generation and tone mapping steps to produce detail preserving image for display on standard dynamic range display devices. Moreover, our technique is effective for blending flash/no-flash image pair and multifocus images, that is, images focused on different targets.

Single-source remote sensing object detection using optical or SAR images struggles in complex environments. Optical images offer rich textural details but are often affected by low-light, cloud-obscured, or low-resolution conditions, reducing the detection performance. SAR images are robust to weather, but suffer from speckle noise and limited semantic expressiveness. Optical and SAR images provide complementary advantages, and fusing them can significantly improve the detection accuracy. However, progress in this field is hindered by the lack of large-scale, standardized datasets. To address these challenges, we propose the first comprehensive dataset for optical-SAR fusion object detection, named Multi-resolution, Multi-polarization, Multi-scene, Multi-source SAR dataset (M4-SAR). It contains 112,184 precisely aligned image pairs and nearly one million labeled instances with arbitrary orientations, spanning six key categories. To enable standardized evaluation, we develop a unified benchmarking toolkit that integrates six state-of-the-art multi-source fusion methods. Furthermore, we propose E2E-OSDet, a novel end-to-end multi-source fusion detection framework that mitigates cross-domain discrepancies and establishes a robust baseline for future studies. Extensive experiments on M4-SAR demonstrate that fusing optical and SAR data can improve mAP by 5.7\% over single-source inputs, with particularly significant gains in complex environments. The dataset and code are publicly available at https://github.com/wchao0601/M4-SAR.

The 3D Gaussian Splatting (3DGS) gained its popularity recently by combining the advantages of both primitive-based and volumetric 3D representations, resulting in improved quality and efficiency for 3D scene rendering. However, 3DGS is not alias-free, and its rendering at varying resolutions could produce severe blurring or jaggies. This is because 3DGS treats each pixel as an isolated, single point rather than as an area, causing insensitivity to changes in the footprints of pixels. Consequently, this discrete sampling scheme inevitably results in aliasing, owing to the restricted sampling bandwidth. In this paper, we derive an analytical solution to address this issue. More specifically, we use a conditioned logistic function as the analytic approximation of the cumulative distribution function (CDF) in a one-dimensional Gaussian signal and calculate the Gaussian integral by subtracting the CDFs. We then introduce this approximation in the two-dimensional pixel shading, and present Analytic-Splatting, which analytically approximates the Gaussian integral within the 2D-pixel window area to better capture the intensity response of each pixel. Moreover, we use the approximated response of the pixel window integral area to participate in the transmittance calculation of volume rendering, making Analytic-Splatting sensitive to the changes in pixel footprint at different resolutions. Experiments on various datasets validate that our approach has better anti-aliasing capability that gives more details and better fidelity.

The recent advancements in 3D Gaussian splatting (3D-GS) have not only facilitated real-time rendering through modern GPU rasterization pipelines but have also attained state-of-the-art rendering quality. Nevertheless, despite its exceptional rendering quality and performance on standard datasets, 3D-GS frequently encounters difficulties in accurately modeling specular and anisotropic components. This issue stems from the limited ability of spherical harmonics (SH) to represent high-frequency information. To overcome this challenge, we introduce Spec-Gaussian, an approach that utilizes an anisotropic spherical Gaussian (ASG) appearance field instead of SH for modeling the view-dependent appearance of each 3D Gaussian. Additionally, we have developed a coarse-to-fine training strategy to improve learning efficiency and eliminate floaters caused by overfitting in real-world scenes. Our experimental results demonstrate that our method surpasses existing approaches in terms of rendering quality. Thanks to ASG, we have significantly improved the ability of 3D-GS to model scenes with specular and anisotropic components without increasing the number of 3D Gaussians. This improvement extends the applicability of 3D GS to handle intricate scenarios with specular and anisotropic surfaces.

A mixed Gaussian fractional process {Y(t)}_{t Bbb R} = {PX(t)}_{t Bbb R} is a multivariate stochastic process obtained by pre-multiplying a vector of independent, Gaussian fractional process entries X by a nonsingular matrix P. It is interpreted that Y is observable, while X is a hidden process occurring in an (unknown) system of coordinates P. Mixed processes naturally arise as approximations to solutions of physically relevant classes of multivariate fractional SDEs under aggregation. We propose a semiparametric two-step wavelet-based method for estimating both the demixing matrix P^{-1} and the memory parameters of X. The asymptotic normality of the estimators is established both in continuous and discrete time. Monte Carlo experiments show that the finite sample estimation performance is comparable to that of parametric methods, while being very computationally efficient. As applications, we model a bivariate time series of annual tree ring width measurements, and establish the asymptotic normality of the eigenstructure of sample wavelet matrices.

Echocardiography has been a prominent tool for the diagnosis of cardiac disease. However, these diagnoses can be heavily impeded by poor image quality. Acoustic clutter emerges due to multipath reflections imposed by layers of skin, subcutaneous fat, and intercostal muscle between the transducer and heart. As a result, haze and other noise artifacts pose a real challenge to cardiac ultrasound imaging. In many cases, especially with difficult-to-image patients such as patients with obesity, a diagnosis from B-Mode ultrasound imaging is effectively rendered unusable, forcing sonographers to resort to contrast-enhanced ultrasound examinations or refer patients to other imaging modalities. Tissue harmonic imaging has been a popular approach to combat haze, but in severe cases is still heavily impacted by haze. Alternatively, denoising algorithms are typically unable to remove highly structured and correlated noise, such as haze. It remains a challenge to accurately describe the statistical properties of structured haze, and develop an inference method to subsequently remove it. Diffusion models have emerged as powerful generative models and have shown their effectiveness in a variety of inverse problems. In this work, we present a joint posterior sampling framework that combines two separate diffusion models to model the distribution of both clean ultrasound and haze in an unsupervised manner. Furthermore, we demonstrate techniques for effectively training diffusion models on radio-frequency ultrasound data and highlight the advantages over image data. Experiments on both in-vitro and in-vivo cardiac datasets show that the proposed dehazing method effectively removes haze while preserving signals from weakly reflected tissue.

Capturing high-quality images from only a few detected photons is a fundamental challenge in computational imaging. Single-photon avalanche diode (SPAD) sensors promise high-quality imaging in regimes where conventional cameras fail, but raw quanta frames contain only sparse, noisy, binary photon detections. Recovering a coherent image from a burst of such frames requires handling alignment, denoising, and demosaicing (for color) under noise statistics far outside those assumed by standard restoration pipelines or modern generative models. We present an approach that adapts large text-to-image latent diffusion models to the photon-limited domain of quanta burst imaging. Our method leverages the structural and semantic priors of internet-scale diffusion models while introducing mechanisms to handle Bernoulli photon statistics. By integrating latent-space restoration with burst-level spatio-temporal reasoning, our approach produces reconstructions that are both photometrically faithful and perceptually pleasing, even under high-speed motion. We evaluate the method on synthetic benchmarks and new real-world datasets, including the first color SPAD burst dataset and a challenging Deforming (XD) video benchmark. Across all settings, the approach substantially improves perceptual quality over classical and modern learning-based baselines, demonstrating the promise of adapting large generative priors to extreme photon-limited sensing. Code at https://github.com/Aryan-Garg/gQIR{https://github.com/Aryan-Garg/gQIR}.

Source separation involves the ill-posed problem of retrieving a set of source signals that have been observed through a mixing operator. Solving this problem requires prior knowledge, which is commonly incorporated by imposing regularity conditions on the source signals, or implicitly learned through supervised or unsupervised methods from existing data. While data-driven methods have shown great promise in source separation, they often require large amounts of data, which rarely exists in planetary space missions. To address this challenge, we propose an unsupervised source separation scheme for domains with limited data access that involves solving an optimization problem in the wavelet scattering covariance representation spacex2014an interpretable, low-dimensional representation of stationary processes. We present a real-data example in which we remove transient, thermally-induced microtiltsx2014known as glitchesx2014from data recorded by a seismometer during NASA's InSight mission on Mars. Thanks to the wavelet scattering covariances' ability to capture non-Gaussian properties of stochastic processes, we are able to separate glitches using only a few glitch-free data snippets.

Synthetic Aperture Radar (SAR) imagery plays a critical role in all-weather, day-and-night remote sensing applications. However, existing SAR-oriented deep learning is constrained by data scarcity, while the physically grounded speckle noise in SAR imagery further hampers fine-grained semantic representation learning. To address these challenges, we propose SARMAE, a Noise-Aware Masked Autoencoder for self-supervised SAR representation learning. Specifically, we construct SAR-1M, the first million-scale SAR dataset, with additional paired optical images, to enable large-scale pre-training. Building upon this, we design Speckle-Aware Representation Enhancement (SARE), which injects SAR-specific speckle noise into masked autoencoders to facilitate noise-aware and robust representation learning. Furthermore, we introduce Semantic Anchor Representation Constraint (SARC), which leverages paired optical priors to align SAR features and ensure semantic consistency. Extensive experiments across multiple SAR datasets demonstrate that SARMAE achieves state-of-the-art performance on classification, detection, and segmentation tasks. Code and models will be available at https://github.com/MiliLab/SARMAE.

We develop a novel way to probe subgalactic-scale matter distribution with diffractive lensing on gravitational waves. Five-year observations from Einstein Telescope and DECIGO are expected to probe k= 10^5sim 10^8 ,{rm Mpc}^{-1} down to P(k) = 10^{-16} sim 10^{-14} ,{rm Mpc}^3 level. These results can be interpreted in terms of primordial black holes in the range M_{rm PBH} gtrsim 10^{-3}M_odot down to f_{rm PBH} = 10^{-6} level, or QCD axion minihalos in the range m_a = 10^{-3} sim 10^{-12} ,{rm eV}. A key result of the paper is the approximate relation between the scale k and the gravitational wave frequency f, derived in an ensemble of `multi-lensing' events. This relation enables direct measurement of the power spectrum at specific scales, with sensitivities characterized by model-independent kernels delta P(k). Additionally, we delineate the statistical properties of `multi-lensing' based on the `Fresnel number' N_F. When N_F cal O(1), the statistical significance can be approximately calculated by Variance of lensing effects, which is directly related to the power spectrum among other moments of matter distribution.

In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise. Our solution incorporates ideas from Langevin dynamics and Newton's method, and exploits a pre-trained minimum mean squared error (MMSE) Gaussian denoiser. The proposed approach relies on an intricate derivation of the posterior score function that includes a singular value decomposition (SVD) of the degradation operator, in order to obtain a tractable iterative algorithm for the desired sampling. Due to its stochasticity, the algorithm can produce multiple high perceptual quality samples for the same noisy observation. We demonstrate the abilities of the proposed paradigm for image deblurring, super-resolution, and compressive sensing. We show that the samples produced are sharp, detailed and consistent with the given measurements, and their diversity exposes the inherent uncertainty in the inverse problem being solved.

Laser cutting is a widely adopted technology in material processing across various industries, but it generates a significant amount of dust, smoke, and aerosols during operation, posing a risk to both the environment and workers' health. Speckle sensing has emerged as a promising method to monitor the cutting process and identify material types in real-time. This paper proposes a material classification technique using a speckle pattern of the material's surface based on deep learning to monitor and control the laser cutting process. The proposed method involves training a convolutional neural network (CNN) on a dataset of laser speckle patterns to recognize distinct material types for safe and efficient cutting. Previous methods for material classification using speckle sensing may face issues when the color of the laser used to produce the speckle pattern is changed. Experiments conducted in this study demonstrate that the proposed method achieves high accuracy in material classification, even when the laser color is changed. The model achieved an accuracy of 98.30 % on the training set and 96.88% on the validation set. Furthermore, the model was evaluated on a set of 3000 new images for 30 different materials, achieving an F1-score of 0.9643. The proposed method provides a robust and accurate solution for material-aware laser cutting using speckle sensing.

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the varphi^4 model and weak lensing convergence maps with higher resolution than in previous works.

Poisson noise suppression is an important preprocessing step in several applications, such as medical imaging, microscopy, and astronomical imaging. In this work, we propose a novel patch-wise Poisson noise removal strategy, in which the MMSE estimator is utilized in order to produce the denoising result for each image patch. Fast and accurate computation of the MMSE estimator is carried out using k-d tree search followed by search in the K-nearest neighbor graph. Our experiments show that the proposed method is the preferable choice for low signal-to-noise ratios.

Ultra-High-Definition (UHD) photo has gradually become the standard configuration in advanced imaging devices. The new standard unveils many issues in existing approaches for low-light image enhancement (LLIE), especially in dealing with the intricate issue of joint luminance enhancement and noise removal while remaining efficient. Unlike existing methods that address the problem in the spatial domain, we propose a new solution, UHDFour, that embeds Fourier transform into a cascaded network. Our approach is motivated by a few unique characteristics in the Fourier domain: 1) most luminance information concentrates on amplitudes while noise is closely related to phases, and 2) a high-resolution image and its low-resolution version share similar amplitude patterns.Through embedding Fourier into our network, the amplitude and phase of a low-light image are separately processed to avoid amplifying noise when enhancing luminance. Besides, UHDFour is scalable to UHD images by implementing amplitude and phase enhancement under the low-resolution regime and then adjusting the high-resolution scale with few computations. We also contribute the first real UHD LLIE dataset, UHD-LL, that contains 2,150 low-noise/normal-clear 4K image pairs with diverse darkness and noise levels captured in different scenarios. With this dataset, we systematically analyze the performance of existing LLIE methods for processing UHD images and demonstrate the advantage of our solution. We believe our new framework, coupled with the dataset, would push the frontier of LLIE towards UHD. The code and dataset are available at https://li-chongyi.github.io/UHDFour.

Modeling latent variables with priors and hyperpriors is an essential problem in variational image compression. Formally, trade-off between rate and distortion is handled well if priors and hyperpriors precisely describe latent variables. Current practices only adopt univariate priors and process each variable individually. However, we find inter-correlations and intra-correlations exist when observing latent variables in a vectorized perspective. These findings reveal visual redundancies to improve rate-distortion performance and parallel processing ability to speed up compression. This encourages us to propose a novel vectorized prior. Specifically, a multivariate Gaussian mixture is proposed with means and covariances to be estimated. Then, a novel probabilistic vector quantization is utilized to effectively approximate means, and remaining covariances are further induced to a unified mixture and solved by cascaded estimation without context models involved. Furthermore, codebooks involved in quantization are extended to multi-codebooks for complexity reduction, which formulates an efficient compression procedure. Extensive experiments on benchmark datasets against state-of-the-art indicate our model has better rate-distortion performance and an impressive 3.18times compression speed up, giving us the ability to perform real-time, high-quality variational image compression in practice. Our source code is publicly available at https://github.com/xiaosu-zhu/McQuic.

Cascaded models are multi-scale generative models with a marked capacity for producing perceptually impressive samples at high resolutions. In this work, we show that they can also be excellent likelihood models, so long as we overcome a fundamental difficulty with probabilistic multi-scale models: the intractability of the likelihood function. Chiefly, in cascaded models each intermediary scale introduces extraneous variables that cannot be tractably marginalized out for likelihood evaluation. This issue vanishes by modeling the diffusion process on latent spaces induced by a class of transformations we call hierarchical volume-preserving maps, which decompose spatially structured data in a hierarchical fashion without introducing local distortions in the latent space. We demonstrate that two such maps are well-known in the literature for multiscale modeling: Laplacian pyramids and wavelet transforms. Not only do such reparameterizations allow the likelihood function to be directly expressed as a joint likelihood over the scales, we show that the Laplacian pyramid and wavelet transform also produces significant improvements to the state-of-the-art on a selection of benchmarks in likelihood modeling, including density estimation, lossless compression, and out-of-distribution detection. Investigating the theoretical basis of our empirical gains we uncover deep connections to score matching under the Earth Mover's Distance (EMD), which is a well-known surrogate for perceptual similarity. Code can be found at https://github.com/lihenryhfl/pcdm{this https url}.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

We propose an adaptive training scheme for unsupervised medical image registration. Existing methods rely on image reconstruction as the primary supervision signal. However, nuisance variables (e.g. noise and covisibility), violation of the Lambertian assumption in physical waves (e.g. ultrasound), and inconsistent image acquisition can all cause a loss of correspondence between medical images. As the unsupervised learning scheme relies on intensity constancy between images to establish correspondence for reconstruction, this introduces spurious error residuals that are not modeled by the typical training objective. To mitigate this, we propose an adaptive framework that re-weights the error residuals with a correspondence scoring map during training, preventing the parametric displacement estimator from drifting away due to noisy gradients, which leads to performance degradation. To illustrate the versatility and effectiveness of our method, we tested our framework on three representative registration architectures across three medical image datasets along with other baselines. Our adaptive framework consistently outperforms other methods both quantitatively and qualitatively. Paired t-tests show that our improvements are statistically significant. Code available at: https://voldemort108x.github.io/AdaCS/.

The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where (a) the number of unknowns may potentially be larger than the number of observations and (b) f* admits a sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

Through gravitational lensing, galaxy clusters can magnify supernovae (SNe) and create multiple images of the same SN. This enables measurements of cosmological parameters, which will be increasingly important in light of upcoming telescopic surveys. We study the prospects of detecting strongly lensed SNe in cluster fields with the Nancy Grace Roman Space Telescope (Roman)'s High Latitude Time Domain Survey (HLTDS) and the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST). We employed two approaches: one focusing on known multiply imaged galaxies behind clusters, along with the SN rates specific to those galaxies, and another based on the expected number of lensed SNe exploding in a given volume behind a galaxy cluster. We collected all the clusters in the literature that feature a well-constrained lens model and multiply imaged galaxies behind clusters with high-quality data for the lensed galaxies. This allowed us to determine the SN rate for each galaxy. We provide predictions for 46 clusters visible to the Vera C. Rubin Observatory, as well as for 9 observable by Roman's HLTDS, depending on whether the clusters fall within the survey's observing field. We predict that the number of multiply imaged SNe discovered by LSST in its first three years is 3.95 pm 0.89 from the first approach or 4.94 pm 1.02 from the second. For the HLTDS, the expected number of multiply imaged SNe ranges from 0.38 pm 0.15 to 5.2 pm 2.2, depending on the specific cluster observed, however, the fields to be targeted remain a matter of discussion. We conclude that LSST offers great prospects for detecting multiply imaged SNe. Our predictions are effectively lower limits, as we only considered the most massive and well-studied clusters. We provide a recommendation for HLTDS observing field selection, namely: either MACS J0553.4-3342 or Abell 1758a should be observed by the survey.

This paper is an extended and reworked version of a short course given by the author at ''Uzbekistan-Ukrainian readings in stochastic processes'', Tashkent-Kyiv, 2022, and was prepared for a special issue of ''Theory of stochastic processes'', devoted to publishing lecture notes from the aforementioned workshop. The survey is devoted to operator splitting methods in the abstract formulation and their applications in probability. While the survey is focused on multiplicative methods, the BCH formula is used to discuss exponential splitting methods and a short informal introduction to additive splitting is presented. We introduce frameworks and available deterministic and probabilistic results and concentrate on constructing a wide picture of the field of operator splitting methods, providing a rigorous description in the setting of abstract Cauchy problems and an informal discussion for further and parallel advances. Some limitations and common difficulties are listed, as well as examples of works that provide solutions or hints. No new results are given. The bibliography contains illustrative deterministic examples and a selection of probability-related works.

A surface photographed under even light presents nearly the same appearance from every angle; the same surface under uneven light does not. Exposure changes between views, illumination varies within a single image, and locally strong light sources leave one region bright and its neighbor in shadow. Multi-view reconstruction methods such as 3D Gaussian Splatting treat these lighting artifacts as if they were properties of the scene, entangling capture-specific illumination with the geometry and color they recover. We present EvenSplat, a framework that separates the two. EvenSplat couples an image-space illumination decomposition with an illumination field carried by the Gaussians, so that the same explanation of the lighting is shared between the two-dimensional and three-dimensional views of the scene; a camera-response network and a local exposure-compensation module absorb the global and residual differences that remain across training images. Through extensive experiments across multiple datasets and diverse forms of uneven illumination (cross-view exposure, spatial illumination variation, and high-contrast lighting) on both real-world captured and simulated benchmarks, EvenSplat generally outperforms state-of-the-art methods, particularly under high-contrast illumination.

Gaussian Splatting demonstrates impressive results in multi-view reconstruction based on Gaussian explicit representations. However, the current Gaussian primitives only have a single view-dependent color and an opacity to represent the appearance and geometry of the scene, resulting in a non-compact representation. In this paper, we introduce a new method called SVGS (Spatially Varying Gaussian Splatting) that utilizes spatially varying colors and opacity in a single Gaussian primitive to improve its representation ability. We have implemented bilinear interpolation, movable kernels, and tiny neural networks as spatially varying functions. SVGS employs 2D Gaussian surfels as primitives, which significantly enhances novel-view synthesis while maintaining high-quality geometric reconstruction. This approach is particularly effective in practical applications, as scenes combining complex textures with relatively simple geometry occur frequently in real-world environments. Quantitative and qualitative experimental results demonstrate that all three functions outperform the baseline, with the best movable kernels achieving superior novel view synthesis performance on multiple datasets, highlighting the strong potential of spatially varying functions. Project page: https://ruixu.me/html/SuperGaussians/index.html

Due to the real-time rendering performance, 3D Gaussian Splatting (3DGS) has emerged as the leading method for radiance field reconstruction. However, its reliance on spherical harmonics for color encoding inherently limits its ability to separate diffuse and specular components, making it challenging to accurately represent complex reflections. To address this, we propose a novel enhanced Gaussian kernel that explicitly models specular effects through view-dependent opacity. Meanwhile, we introduce an error-driven compensation strategy to improve rendering quality in existing 3DGS scenes. Our method begins with 2D Gaussian initialization and then adaptively inserts and optimizes enhanced Gaussian kernels, ultimately producing an augmented radiance field. Experiments demonstrate that our method not only surpasses state-of-the-art NeRF methods in rendering performance but also achieves greater parameter efficiency. Project page at: https://xiaoxinyyx.github.io/augs.

Image denoising is a well-known and well studied problem, commonly targeting a minimization of the mean squared error (MSE) between the outcome and the original image. Unfortunately, especially for severe noise levels, such Minimum MSE (MMSE) solutions may lead to blurry output images. In this work we propose a novel stochastic denoising approach that produces viable and high perceptual quality results, while maintaining a small MSE. Our method employs Langevin dynamics that relies on a repeated application of any given MMSE denoiser, obtaining the reconstructed image by effectively sampling from the posterior distribution. Due to its stochasticity, the proposed algorithm can produce a variety of high-quality outputs for a given noisy input, all shown to be legitimate denoising results. In addition, we present an extension of our algorithm for handling the inpainting problem, recovering missing pixels while removing noise from partially given data.

Gradient descent has proven to be a powerful and effective technique for optimization in numerous machine learning applications. Recent advances in computational neuroscience have shown that learning in standard gradient descent optimization formulation is not consistent with learning in biological systems. This has opened up interesting avenues for building biologically inspired learning techniques. One such approach is inspired by Dale's law, which states that inhibitory and excitatory synapses do not swap roles during the course of learning. The resulting exponential gradient descent optimization scheme leads to log-normally distributed synaptic weights. Interestingly, the density that satisfies the Fokker-Planck equation corresponding to the stochastic differential equation (SDE) with geometric Brownian motion (GBM) is the log-normal density. Leveraging this connection, we start with the SDE governing geometric Brownian motion, and show that discretizing the corresponding reverse-time SDE yields a multiplicative update rule, which surprisingly, coincides with the sampling equivalent of the exponential gradient descent update founded on Dale's law. Furthermore, we propose a new formalism for multiplicative denoising score-matching, subsuming the loss function proposed by Hyvaerinen for non-negative data. Indeed, log-normally distributed data is positive and the proposed score-matching formalism turns out to be a natural fit. This allows for training of score-based models for image data and results in a novel multiplicative update scheme for sample generation starting from a log-normal density. Experimental results on MNIST, Fashion MNIST, and Kuzushiji datasets demonstrate generative capability of the new scheme. To the best of our knowledge, this is the first instance of a biologically inspired generative model employing multiplicative updates, founded on geometric Brownian motion.

Generating high-resolution images with generative models has recently been made widely accessible by leveraging diffusion models pre-trained on large-scale datasets. Various techniques, such as MultiDiffusion and SyncDiffusion, have further pushed image generation beyond training resolutions, i.e., from square images to panorama, by merging multiple overlapping diffusion paths or employing gradient descent to maintain perceptual coherence. However, these methods suffer from significant computational inefficiencies due to generating and averaging numerous predictions, which is required in practice to produce high-quality and seamless images. This work addresses this limitation and presents a novel approach that eliminates the need to generate and average numerous overlapping denoising predictions. Our method shifts non-overlapping denoising windows over time, ensuring that seams in one timestep are corrected in the next. This results in coherent, high-resolution images with fewer overall steps. We demonstrate the effectiveness of our approach through qualitative and quantitative evaluations, comparing it with MultiDiffusion, SyncDiffusion, and StitchDiffusion. Our method offers several key benefits, including improved computational efficiency and faster inference times while producing comparable or better image quality.

It is highly desired but challenging to acquire high-quality photos with clear content in low-light environments. Although multi-image processing methods (using burst, dual-exposure, or multi-exposure images) have made significant progress in addressing this issue, they typically focus on specific restoration or enhancement problems, and do not fully explore the potential of utilizing multiple images. Motivated by the fact that multi-exposure images are complementary in denoising, deblurring, high dynamic range imaging, and super-resolution, we propose to utilize exposure bracketing photography to get a high-quality image by combining these tasks in this work. Due to the difficulty in collecting real-world pairs, we suggest a solution that first pre-trains the model with synthetic paired data and then adapts it to real-world unlabeled images. In particular, a temporally modulated recurrent network (TMRNet) and self-supervised adaptation method are proposed. Moreover, we construct a data simulation pipeline to synthesize pairs and collect real-world images from 200 nighttime scenarios. Experiments on both datasets show that our method performs favorably against the state-of-the-art multi-image processing ones. Code and datasets are available at https://github.com/cszhilu1998/BracketIRE.

We present an improvement in the ability to meaningfully track features in high speed videos of Caribbean steelpan drums illuminated by Electronic Speckle Pattern Interferometry (ESPI). This is achieved through the use of up-to-date computer vision libraries for object detection and image segmentation as well as a significant effort toward cleaning the dataset previously used to train systems for this application. Besides improvements on previous metric scores by 10% or more, noteworthy in this project are the introduction of a segmentation-regression map for the entire drum surface yielding interference fringe counts comparable to those obtained via object detection, as well as the accelerated workflow for coordinating the data-cleaning-and-model-training feedback loop for rapid iteration allowing this project to be conducted on a timescale of only 18 days.

In this paper, we introduce Textured-GS, an innovative method for rendering Gaussian splatting that incorporates spatially defined color and opacity variations using Spherical Harmonics (SH). This approach enables each Gaussian to exhibit a richer representation by accommodating varying colors and opacities across its surface, significantly enhancing rendering quality compared to traditional methods. To demonstrate the merits of our approach, we have adapted the Mini-Splatting architecture to integrate textured Gaussians without increasing the number of Gaussians. Our experiments across multiple real-world datasets show that Textured-GS consistently outperforms both the baseline Mini-Splatting and standard 3DGS in terms of visual fidelity. The results highlight the potential of Textured-GS to advance Gaussian-based rendering technologies, promising more efficient and high-quality scene reconstructions.

A vital and rapidly growing application, remote sensing offers vast yet sparsely labeled, spatially aligned multimodal data; this makes self-supervised learning algorithms invaluable. We present CROMA: a framework that combines contrastive and reconstruction self-supervised objectives to learn rich unimodal and multimodal representations. Our method separately encodes masked-out multispectral optical and synthetic aperture radar samples -- aligned in space and time -- and performs cross-modal contrastive learning. Another encoder fuses these sensors, producing joint multimodal encodings that are used to predict the masked patches via a lightweight decoder. We show that these objectives are complementary when leveraged on spatially aligned multimodal data. We also introduce X- and 2D-ALiBi, which spatially biases our cross- and self-attention matrices. These strategies improve representations and allow our models to effectively extrapolate to images up to 17.6x larger at test-time. CROMA outperforms the current SoTA multispectral model, evaluated on: four classification benchmarks -- finetuning (avg. 1.8%), linear (avg. 2.4%) and nonlinear (avg. 1.4%) probing, kNN classification (avg. 3.5%), and K-means clustering (avg. 8.4%); and three segmentation benchmarks (avg. 6.4%). CROMA's rich, optionally multimodal representations can be widely leveraged across remote sensing applications.

Low-light image enhancement (LLIE) aims to restore natural visibility, color fidelity, and structural detail under severe illumination degradation. State-of-the-art (SOTA) LLIE techniques often rely on large models and multi-stage training, limiting practicality for edge deployment. Moreover, their dependence on a single color space introduces instability and visible exposure or color artifacts. To address these, we propose Multinex, an ultra-lightweight structured framework that integrates multiple fine-grained representations within a principled Retinex residual formulation. It decomposes an image into illumination and color prior stacks derived from distinct analytic representations, and learns to fuse these representations into luminance and reflectance adjustments required to correct exposure. By prioritizing enhancement over reconstruction and exploiting lightweight neural operations, Multinex significantly reduces computational cost, exemplified by its lightweight (45K parameters) and nano (0.7K parameters) versions. Extensive benchmarks show that all lightweight variants significantly outperform their corresponding lightweight SOTA models, and reach comparable performance to heavy models. Paper page available at https://albrateanu.github.io/multinex.

Image compression, restoration, and generation all require a way to measure how different two images look to a person. Pixel error ignores how people see, while the most accurate perceptual distances are typically fitted to human judgments, tying them to a fixed data and resolution. For example, when image resolution is doubled, the correlation of DISTS with human scores on TID2013 drops from 0.815 to 0.717. We introduce the Jacobian Lens Distance (JLD), which derives its perceptual geometry from a frozen vision encoder rather than from human labels. JLD combines the locality of early patch features with the perceptual sensitivity captured by later encoder representations. Specifically, we use the encoder Jacobian to identify directions in the early feature space that most strongly affect the encoder output, producing a fixed metric tensor, E[J^top J], which we call the Jacobian lens. The lens is fitted only once from 100 unlabeled images, taking about 35 seconds. Locally, this construction defines a pullback metric in pixel space, giving JLD a clear geometric interpretation that can be directly analyzed on real images. Across four standard perceptual databases, JLD achieves state-of-the-art performance and consistently outperforms LPIPS, DISTS, PieAPP, and DreamSim. JLD is also robust to changes in image resolution, on TID2013, its lens-term correlation remains nearly unchanged when the resolution is doubled, decreasing only from 0.850 to 0.845. We further introduce JLD-fast, which is 4times faster than LPIPS-VGG while achieving a mean correlation of 0.911. Finally, JLD naturally extends to video, reaching a correlation of 0.786 on Waterloo IVC 4K compared with 0.611 for VMAF.

With the advent of surveys like Euclid and Vera C. Rubin, astrophysicists will have access to both deep, high-resolution images and multiband images. However, these two types are not simultaneously available in any single dataset. It is therefore vital to devise image deconvolution algorithms that exploit the best of both worlds and that can jointly analyze datasets spanning a range of resolutions and wavelengths. In this work we introduce a novel multiband deconvolution technique aimed at improving the resolution of ground-based astronomical images by leveraging higher-resolution space-based observations. The method capitalizes on the fortunate fact that the Rubin r, i, and z bands lie within the Euclid VIS band. The algorithm jointly de-convolves all the data to convert the r-, i-, and z-band Rubin images to the resolution of Euclid by leveraging the correlations between the different bands. We also investigate the performance of deep-learning-based denoising with DRUNet to further improve the results. We illustrate the effectiveness of our method in terms of resolution and morphology recovery, flux preservation, and generalization to different noise levels. This approach extends beyond the specific Euclid-Rubin combination, offering a versatile solution to improving the resolution of ground-based images in multiple photometric bands by jointly using any space-based images with overlapping filters.

3D Gaussian Splatting (3DGS) has advanced radiance field reconstruction by enabling real-time rendering. However, its reliance on Gaussian kernels for geometry and low-order Spherical Harmonics (SH) for color encoding limits its ability to capture complex geometries and diverse colors. We introduce Deformable Beta Splatting (DBS), a deformable and compact approach that enhances both geometry and color representation. DBS replaces Gaussian kernels with deformable Beta Kernels, which offer bounded support and adaptive frequency control to capture fine geometric details with higher fidelity while achieving better memory efficiency. In addition, we extended the Beta Kernel to color encoding, which facilitates improved representation of diffuse and specular components, yielding superior results compared to SH-based methods. Furthermore, Unlike prior densification techniques that depend on Gaussian properties, we mathematically prove that adjusting regularized opacity alone ensures distribution-preserved Markov chain Monte Carlo (MCMC), independent of the splatting kernel type. Experimental results demonstrate that DBS achieves state-of-the-art visual quality while utilizing only 45% of the parameters and rendering 1.5x faster than 3DGS-MCMC, highlighting the superior performance of DBS for real-time radiance field rendering. Interactive demonstrations and source code are available on our project website: https://rongliu-leo.github.io/beta-splatting/.

The SIML (abbreviation of Separating Information Maximal Likelihood) method, has been introduced by N. Kunitomo and S. Sato and their collaborators to estimate the integrated volatility of high-frequency data that is assumed to be an It\^o process but with so-called microstructure noise. The SIML estimator turned out to share many properties with the estimator introduced by P. Malliavin and M.E. Mancino. The present paper establishes the consistency and the asymptotic normality under a general sampling scheme but without microstructure noise. Specifically, a fast convergence shown for Malliavin--Mancino estimator by E. Clement and A. Gloter is also established for the SIML estimator.

In-line digital holography (DIH) is a widely used lensless imaging technique, valued for its simplicity and capability to image samples at high throughput. However, capturing only intensity of the interference pattern during the recording process gives rise to some unwanted terms such as cross-term and twin-image. The cross-term can be suppressed by adjusting the intensity of reference wave, but the twin-image problem remains. The twin-image is a spectral artifact that superimposes a defocused conjugate wave onto the reconstructed object, severely degrading image quality. While deep learning has recently emerged as a powerful tool for phase retrieval, traditional Convolutional Neural Networks (CNNs) are limited by their local receptive fields, making them less effective at capturing the global diffraction patterns inherent in holography. In this study, we introduce HoloPASWIN, a physics-aware deep learning framework based on the Swin Transformer architecture. By leveraging hierarchical shifted-window attention, our model efficiently captures both local details and long-range dependencies essential for accurate holographic reconstruction. We propose a comprehensive loss function that integrates frequency-domain constraints with physical consistency via a differentiable angular spectrum propagator, ensuring high spectral fidelity. Validated on a large-scale synthetic dataset of 25,000 samples with diverse noise configurations (speckle, shot, read, and dark noise), HoloPASWIN demonstrates effective twin-image suppression and robust reconstruction quality.

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size n is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in R^K, where samples are assumed to be corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. We prove the existence of an algorithm that with high probability outputs a simplex having a ell_2 distance of at most varepsilon from the true simplex (for any varepsilon>0). Also, we theoretically show that in order to achieve this bound, it is sufficient to have ngeleft(K^2/varepsilon^2right)e^{Omegaleft(K/SNR^2right)} samples, where SNR stands for the signal-to-noise ratio. This result solves an important open problem and shows as long as SNRgeOmegaleft(K^{1/2}right), the sample complexity of the noisy regime has the same order to that of the noiseless case. Our proofs are a combination of the so-called sample compression technique in ashtiani2018nearly, mathematical tools from high-dimensional geometry, and Fourier analysis. In particular, we have proposed a general Fourier-based technique for recovery of a more general class of distribution families from additive Gaussian noise, which can be further used in a variety of other related problems.

3D Gaussian Splatting (3DGS) has gained significant attention for 3D scene reconstruction, but still suffers from complex outdoor environments, especially under adverse weather. This is because 3DGS treats the artifacts caused by adverse weather as part of the scene and will directly reconstruct them, largely reducing the clarity of the reconstructed scene. To address this challenge, we propose WeatherGS, a 3DGS-based framework for reconstructing clear scenes from multi-view images under different weather conditions. Specifically, we explicitly categorize the multi-weather artifacts into the dense particles and lens occlusions that have very different characters, in which the former are caused by snowflakes and raindrops in the air, and the latter are raised by the precipitation on the camera lens. In light of this, we propose a dense-to-sparse preprocess strategy, which sequentially removes the dense particles by an Atmospheric Effect Filter (AEF) and then extracts the relatively sparse occlusion masks with a Lens Effect Detector (LED). Finally, we train a set of 3D Gaussians by the processed images and generated masks for excluding occluded areas, and accurately recover the underlying clear scene by Gaussian splatting. We conduct a diverse and challenging benchmark to facilitate the evaluation of 3D reconstruction under complex weather scenarios. Extensive experiments on this benchmark demonstrate that our WeatherGS consistently produces high-quality, clean scenes across various weather scenarios, outperforming existing state-of-the-art methods. See project page:https://jumponthemoon.github.io/weather-gs.

4D Gaussian Splatting (4DGS) has recently emerged as a promising technique for capturing complex dynamic 3D scenes with high fidelity. It utilizes a 4D Gaussian representation and a GPU-friendly rasterizer, enabling rapid rendering speeds. Despite its advantages, 4DGS faces significant challenges, notably the requirement of millions of 4D Gaussians, each with extensive associated attributes, leading to substantial memory and storage cost. This paper introduces a memory-efficient framework for 4DGS. We streamline the color attribute by decomposing it into a per-Gaussian direct color component with only 3 parameters and a shared lightweight alternating current color predictor. This approach eliminates the need for spherical harmonics coefficients, which typically involve up to 144 parameters in classic 4DGS, thereby creating a memory-efficient 4D Gaussian representation. Furthermore, we introduce an entropy-constrained Gaussian deformation technique that uses a deformation field to expand the action range of each Gaussian and integrates an opacity-based entropy loss to limit the number of Gaussians, thus forcing our model to use as few Gaussians as possible to fit a dynamic scene well. With simple half-precision storage and zip compression, our framework achieves a storage reduction by approximately 190times and 125times on the Technicolor and Neural 3D Video datasets, respectively, compared to the original 4DGS. Meanwhile, it maintains comparable rendering speeds and scene representation quality, setting a new standard in the field. Code is available at https://github.com/Xinjie-Q/MEGA.

Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for Gaussian and mildly non-Gaussian fields. In this paper we extend the formulae to composite fields which are sums of two fields and explicitly derive the expressions for the sum of uncorrelated mildly non-Gaussian and Gaussian fields. These formulae are applicable to observed data which is usually a sum of the true signal and one or more secondary fields that can be either noise, or some residual contaminating signal. Our formulae provide explicit quantification of the effect of the secondary field on the morphology and statistical nature of the true signal. As examples, we apply the formulae to determine how the presence of Gaussian noise can bias the morphological properties and statistical nature of Gaussian and non-Gaussian CMB temperature maps.

Tweedie distributions are a special case of exponential dispersion models, which are often used in classical statistics as distributions for generalized linear models. Here, we reveal that Tweedie distributions also play key roles in modern deep learning era, leading to a distribution independent self-supervised image denoising formula without clean reference images. Specifically, by combining with the recent Noise2Score self-supervised image denoising approach and the saddle point approximation of Tweedie distribution, we can provide a general closed-form denoising formula that can be used for large classes of noise distributions without ever knowing the underlying noise distribution. Similar to the original Noise2Score, the new approach is composed of two successive steps: score matching using perturbed noisy images, followed by a closed form image denoising formula via distribution-independent Tweedie's formula. This also suggests a systematic algorithm to estimate the noise model and noise parameters for a given noisy image data set. Through extensive experiments, we demonstrate that the proposed method can accurately estimate noise models and parameters, and provide the state-of-the-art self-supervised image denoising performance in the benchmark dataset and real-world dataset.

We present GaSLight, a method that generates spatially-varying lighting from regular images. Our method proposes using HDR Gaussian Splats as light source representation, marking the first time regular images can serve as light sources in a 3D renderer. Our two-stage process first enhances the dynamic range of images plausibly and accurately by leveraging the priors embedded in diffusion models. Next, we employ Gaussian Splats to model 3D lighting, achieving spatially variant lighting. Our approach yields state-of-the-art results on HDR estimations and their applications in illuminating virtual objects and scenes. To facilitate the benchmarking of images as light sources, we introduce a novel dataset of calibrated and unsaturated HDR to evaluate images as light sources. We assess our method using a combination of this novel dataset and an existing dataset from the literature. Project page: https://lvsn.github.io/gaslight/

Despite the proven significance of hyperspectral images (HSIs) in performing various computer vision tasks, its potential is adversely affected by the low-resolution (LR) property in the spatial domain, resulting from multiple physical factors. Inspired by recent advancements in deep generative models, we propose an HSI Super-resolution (SR) approach with Conditional Diffusion Models (HSR-Diff) that merges a high-resolution (HR) multispectral image (MSI) with the corresponding LR-HSI. HSR-Diff generates an HR-HSI via repeated refinement, in which the HR-HSI is initialized with pure Gaussian noise and iteratively refined. At each iteration, the noise is removed with a Conditional Denoising Transformer (CDF ormer) that is trained on denoising at different noise levels, conditioned on the hierarchical feature maps of HR-MSI and LR-HSI. In addition, a progressive learning strategy is employed to exploit the global information of full-resolution images. Systematic experiments have been conducted on four public datasets, demonstrating that HSR-Diff outperforms state-of-the-art methods.

The antenna-elements that make up a radio interferometer form a spatial filter that samples components of the Fourier transform of a target radio astronomical source brightness. Along the signal path, there are multiplicative and additive perturbation effects that alter the signal and that should be corrected. The process of mitigating these perturbation effects is called calibration. In this work, we develop a new and fast Maximum Likelihood based estimator of these perturbation effects using the Exponential Map and Lie groups. To evaluate its performance, we compare it to the Cramér-Rao Lower Bound and, to test the estimation time, we compare it with the Expectation Maximization algorithm, another fast Maximum Likelihood estimator. Finally, we apply our estimator to a real observation of the protoplanetary disk AS 209 made with the Submillimeter Array. We found that our proposed estimator meets the Cramér-Rao Lower Bound and it was approximately 40 times faster than the Expectation Maximization algorithm.

Fix a strip width \(ρ>0\), a Diophantine frequency \(α\), an integer \(N\ge2\), and \(λ>1\). For the family \[ V_{\varepsilon,δ}(x) =2λ\cos(2πN x)+\varepsilonδ(x), \] we prove that there is an open prevalent set \(\mathcal P_{\rm strat}\) of real-analytic strip-\(ρ\) perturbations such that every \(δ\in\mathcal P_{\rm strat}\) admits \(\varepsilon_0(δ)>0\) for which \[ gathered Leb\left\{ E\inΣ(V_{\varepsilon,δ},α): ω(α,E;V_{\varepsilon,δ})=s \right\}>0, 0<\varepsilon<\varepsilon_0(δ), \qquad s=1,\ldots,N. gathered \] The proof relates acceleration to the total multiplicity of real zeros of analytic overlap coefficients for first-return cocycles. Under quantitative control of the return products, Poisson integration and Kac normalization identify acceleration with half this multiplicity. A positive analytic dual state gives the finite-volume spectral gaps and Schur curvature needed at the upper spectral edge. Schur variations separate the perturbed maxima, and parameter exclusion preserves \(s\) pairs of simple zeros on a positive-measure spectral set.

3D Gaussian Splatting is a new method for modeling and rendering 3D radiance fields that achieves much faster learning and rendering time compared to SOTA NeRF methods. However, it comes with a drawback in the much larger storage demand compared to NeRF methods since it needs to store the parameters for several 3D Gaussians. We notice that many Gaussians may share similar parameters, so we introduce a simple vector quantization method based on \kmeans algorithm to quantize the Gaussian parameters. Then, we store the small codebook along with the index of the code for each Gaussian. Moreover, we compress the indices further by sorting them and using a method similar to run-length encoding. We do extensive experiments on standard benchmarks as well as a new benchmark which is an order of magnitude larger than the standard benchmarks. We show that our simple yet effective method can reduce the storage cost for the original 3D Gaussian Splatting method by a factor of almost 20times with a very small drop in the quality of rendered images.

Scene reconstruction in the presence of high-speed motion and low illumination is important in many applications such as augmented and virtual reality, drone navigation, and autonomous robotics. Traditional motion estimation techniques fail in such conditions, suffering from too much blur in the presence of high-speed motion and strong noise in low-light conditions. Single-photon cameras have recently emerged as a promising technology capable of capturing hundreds of thousands of photon frames per second thanks to their high speed and extreme sensitivity. Unfortunately, traditional computer vision techniques are not well suited for dealing with the binary-valued photon data captured by these cameras because these are corrupted by extreme Poisson noise. Here we present a method capable of estimating extreme scene motion under challenging conditions, such as low light or high dynamic range, from a sequence of high-speed image frames such as those captured by a single-photon camera. Our method relies on iteratively improving a motion estimate by grouping and aggregating frames after-the-fact, in a stratified manner. We demonstrate the creation of high-quality panoramas under fast motion and extremely low light, and super-resolution results using a custom single-photon camera prototype. For code and supplemental material see our https://wisionlab.com/project/panoramas-from-photons/{project webpage}.

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we propose an innovative second-order algorithm that employs a Newton-type method with hard thresholding. This algorithm overcomes the linear convergence limitations of first-order methods while preserving their hallmark per-iteration computational efficiency. We provide theoretical guarantees that our algorithm converges to the s-sparse ground truth signal x^{natural} in R^n (up to a global sign) at a quadratic convergence rate after at most O(log (Vertx^{natural} Vert /x_{min}^{natural})) iterations, using Omega(s^2log n) Gaussian random samples. Numerical experiments show that our algorithm achieves a significantly faster convergence rate than state-of-the-art methods.

We train an object detector built from convolutional neural networks to count interference fringes in elliptical antinode regions in frames of high-speed video recordings of transient oscillations in Caribbean steelpan drums illuminated by electronic speckle pattern interferometry (ESPI). The annotations provided by our model aim to contribute to the understanding of time-dependent behavior in such drums by tracking the development of sympathetic vibration modes. The system is trained on a dataset of crowdsourced human-annotated images obtained from the Zooniverse Steelpan Vibrations Project. Due to the small number of human-annotated images and the ambiguity of the annotation task, we also evaluate the model on a large corpus of synthetic images whose properties have been matched to the real images by style transfer using a Generative Adversarial Network. Applying the model to thousands of unlabeled video frames, we measure oscillations consistent with audio recordings of these drum strikes. One unanticipated result is that sympathetic oscillations of higher-octave notes significantly precede the rise in sound intensity of the corresponding second harmonic tones; the mechanism responsible for this remains unidentified. This paper primarily concerns the development of the predictive model; further exploration of the steelpan images and deeper physical insights await its further application.

Low-light image enhancement techniques have significantly progressed, but unstable image quality recovery and unsatisfactory visual perception are still significant challenges. To solve these problems, we propose a novel and robust low-light image enhancement method via CLIP-Fourier Guided Wavelet Diffusion, abbreviated as CFWD. Specifically, CFWD leverages multimodal visual-language information in the frequency domain space created by multiple wavelet transforms to guide the enhancement process. Multi-scale supervision across different modalities facilitates the alignment of image features with semantic features during the wavelet diffusion process, effectively bridging the gap between degraded and normal domains. Moreover, to further promote the effective recovery of the image details, we combine the Fourier transform based on the wavelet transform and construct a Hybrid High Frequency Perception Module (HFPM) with a significant perception of the detailed features. This module avoids the diversity confusion of the wavelet diffusion process by guiding the fine-grained structure recovery of the enhancement results to achieve favourable metric and perceptually oriented enhancement. Extensive quantitative and qualitative experiments on publicly available real-world benchmarks show that our approach outperforms existing state-of-the-art methods, achieving significant progress in image quality and noise suppression. The project code is available at https://github.com/hejh8/CFWD.

In metrology, Fisher information is an important metric that quantifies the precision that can be achieved in a measurement. For optical measurements using coherent light it has been shown that Fisher information can be expressed simply using the scattering matrix of the system. Fisher information can be maximized over the input modes to achieve maximum information states, which produce optimally precise estimates for a parameter when the system is limited by photon noise. Here, we extend this approach to multiparameter estimation, in which case Fisher information takes the form of a matrix. We consider several scalar functions of the Fisher matrix to optimize the precision in multiple parameters at the same time. We also consider strategies for dealing with nuisance parameters, which can degrade the achievable precision of other parameters but are not of interest to measure. We corroborate our findings numerically using a scattering system of 2D coupled dipoles.

We present a spatial and angular Gaussian based representation and a triple splatting process, for real-time, high-quality novel lighting-and-view synthesis from multi-view point-lit input images. To describe complex appearance, we employ a Lambertian plus a mixture of angular Gaussians as an effective reflectance function for each spatial Gaussian. To generate self-shadow, we splat all spatial Gaussians towards the light source to obtain shadow values, which are further refined by a small multi-layer perceptron. To compensate for other effects like global illumination, another network is trained to compute and add a per-spatial-Gaussian RGB tuple. The effectiveness of our representation is demonstrated on 30 samples with a wide variation in geometry (from solid to fluffy) and appearance (from translucent to anisotropic), as well as using different forms of input data, including rendered images of synthetic/reconstructed objects, photographs captured with a handheld camera and a flash, or from a professional lightstage. We achieve a training time of 40-70 minutes and a rendering speed of 90 fps on a single commodity GPU. Our results compare favorably with state-of-the-art techniques in terms of quality/performance. Our code and data are publicly available at https://GSrelight.github.io/.

Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (\ie the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory-efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser. Code and examples are available on the project webpage in https://hilamanor.github.io/GaussianDenoisingPosterior/ .

Image similarity metrics play an important role in computer vision applications, as they are used in image processing, computer vision and machine learning. Furthermore, those metrics enable tasks such as image retrieval, object recognition and quality assessment, essential in fields like healthcare, astronomy and surveillance. Existing metrics, such as PSNR, MSE, SSIM, ISSM and FSIM, often face limitations in terms of either speed, complexity or sensitivity to small changes in images. To address these challenges, a novel image similarity metric, namely CSIM, that combines real-time while being sensitive to subtle image variations is investigated in this paper. The novel metric uses Gaussian Copula from probability theory to transform an image into vectors of pixel distribution associated to local image patches. These vectors contain, in addition to intensities and pixel positions, information on the dependencies between pixel values, capturing the structural relationships within the image. By leveraging the properties of Copulas, CSIM effectively models the joint distribution of pixel intensities, enabling a more nuanced comparison of image patches making it more sensitive to local changes compared to other metrics. Experimental results demonstrate that CSIM outperforms existing similarity metrics in various image distortion scenarios, including noise, compression artifacts and blur. The metric's ability to detect subtle differences makes it suitable for applications requiring high precision, such as medical imaging, where the detection of minor anomalies can be of a high importance. The results obtained in this work can be reproduced from this Github repository: https://github.com/safouaneelg/copulasimilarity.

Ultrasound (US) imaging poses unique challenges for representation learning due to its inherently noisy acquisition process. The low signal-to-noise ratio and stochastic speckle patterns hinder standard self-supervised learning methods relying on a pixel-level reconstruction objective. Joint-Embedding Predictive Architectures (JEPAs) address this drawback by predicting masked latent representations rather than raw pixels. However, standard approaches depend on hyperparameter-brittle and computationally expensive online teachers updated via exponential moving average. We propose US-JEPA, a self-supervised framework that adopts the Static-teacher Asymmetric Latent Training (SALT) objective. By using a frozen, domain-specific teacher to provide stable latent targets, US-JEPA decouples student-teacher optimization and pushes the student to expand upon the semantic priors of the teacher. In addition, we provide the first rigorous comparison of all publicly available state-of-the-art ultrasound foundation models on UltraBench, a public dataset benchmark spanning multiple organs and pathological conditions. Under linear probing for diverse classification tasks, US-JEPA achieves performance competitive with or superior to domain-specific and universal vision foundation model baselines. Our results demonstrate that masked latent prediction provides a stable and efficient path toward robust ultrasound representations.

Convolution is a broadly useful operation with applications including signal processing, machine learning, probability, optics, polynomial multiplication, and efficient parsing. Usually, however, this operation is understood and implemented in more specialized forms, hiding commonalities and limiting usefulness. This paper formulates convolution in the common algebraic framework of semirings and semimodules and populates that framework with various representation types. One of those types is the grand abstract template and itself generalizes to the free semimodule monad. Other representations serve varied uses and performance trade-offs, with implementations calculated from simple and regular specifications. Of particular interest is Brzozowski's method for regular expression matching. Uncovering the method's essence frees it from syntactic manipulations, while generalizing from boolean to weighted membership (such as multisets and probability distributions) and from sets to n-ary relations. The classic trie data structure then provides an elegant and efficient alternative to syntax. Pleasantly, polynomial arithmetic requires no additional implementation effort, works correctly with a variety of representations, and handles multivariate polynomials and power series with ease. Image convolution also falls out as a special case.

Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go, and image captioning. Many of these applications first perform feature extraction and then feed the results thereof into a trainable classifier. The mathematical analysis of deep convolutional neural networks for feature extraction was initiated by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on a wavelet transform followed by the modulus non-linearity in each network layer, and proved translation invariance (asymptotically in the wavelet scale parameter) and deformation stability of the corresponding feature extractor. This paper complements Mallat's results by developing a theory that encompasses general convolutional transforms, or in more technical parlance, general semi-discrete frames (including Weyl-Heisenberg filters, curvelets, shearlets, ridgelets, wavelets, and learned filters), general Lipschitz-continuous non-linearities (e.g., rectified linear units, shifted logistic sigmoids, hyperbolic tangents, and modulus functions), and general Lipschitz-continuous pooling operators emulating, e.g., sub-sampling and averaging. In addition, all of these elements can be different in different network layers. For the resulting feature extractor we prove a translation invariance result of vertical nature in the sense of the features becoming progressively more translation-invariant with increasing network depth, and we establish deformation sensitivity bounds that apply to signal classes such as, e.g., band-limited functions, cartoon functions, and Lipschitz functions.

High dynamic range (HDR) imaging involves capturing a series of frames of the same scene, each with different exposure settings, to broaden the dynamic range of light. This can be achieved through burst capturing or using staggered HDR sensors that capture long and short exposures simultaneously in the camera image signal processor (ISP). Within camera ISP pipeline, illuminant estimation is a crucial step aiming to estimate the color of the global illuminant in the scene. This estimation is used in camera ISP white-balance module to remove undesirable color cast in the final image. Despite the multiple frames captured in the HDR pipeline, conventional illuminant estimation methods often rely only on a single frame of the scene. In this paper, we explore leveraging information from frames captured with different exposure times. Specifically, we introduce a simple feature extracted from dual-exposure images to guide illuminant estimators, referred to as the dual-exposure feature (DEF). To validate the efficiency of DEF, we employed two illuminant estimators using the proposed DEF: 1) a multilayer perceptron network (MLP), referred to as exposure-based MLP (EMLP), and 2) a modified version of the convolutional color constancy (CCC) to integrate our DEF, that we call ECCC. Both EMLP and ECCC achieve promising results, in some cases surpassing prior methods that require hundreds of thousands or millions of parameters, with only a few hundred parameters for EMLP and a few thousand parameters for ECCC.

Improving the quality of hyperspectral images (HSIs), such as through super-resolution, is a crucial research area. However, generative modeling for HSIs presents several challenges. Due to their high spectral dimensionality, HSIs are too memory-intensive for direct input into conventional diffusion models. Furthermore, general generative models lack an understanding of the topological and geometric structures of ground objects in remote sensing imagery. In addition, most diffusion models optimize loss functions at the noise level, leading to a non-intuitive convergence behavior and suboptimal generation quality for complex data. To address these challenges, we propose a Geometric Enhanced Wavelet-based Diffusion Model (GEWDiff), a novel framework for reconstructing hyperspectral images at 4-times super-resolution. A wavelet-based encoder-decoder is introduced that efficiently compresses HSIs into a latent space while preserving spectral-spatial information. To avoid distortion during generation, we incorporate a geometry-enhanced diffusion process that preserves the geometric features. Furthermore, a multi-level loss function was designed to guide the diffusion process, promoting stable convergence and improved reconstruction fidelity. Our model demonstrated state-of-the-art results across multiple dimensions, including fidelity, spectral accuracy, visual realism, and clarity.

Recent advances in camouflaged object detection (COD) have led to substantial progress in challenging low-visibility scenarios, with pioneering studies demonstrating notable success in localizing objects in camouflaged scenes. Despite these achievements, existing approaches predominantly rely on conventional three-channel RGB imagery, thereby constraining the available visual information to a limited spectral range. Multispectral images offer a wide range of information about a scene by capturing fine-grained spectral signatures. Hence, by leveraging multispectral images for COD, we introduce a novel approach to detect camouflaged objects from the corresponding multispectral inputs. In particular, we propose an end-to-end framework, \textit{MSFormer}, that takes a multispectral camouflaged image as input and predicts a binary mask for it. Additionally, we also provide empirical justification for integrating multispectral bands for this complex low-vision task. Our extensive experiments demonstrate the effectiveness of our method, which outperforms existing methods.

Multimodal LLMs can accurately perceive numerical content across modalities yet fail to perform exact multi-digit multiplication when the identical underlying arithmetic problem is presented as numerals, number words, images, or in audio form. Because existing benchmarks often lack systematically paired instances across modalities, it remains difficult to compare genuine arithmetic limits within and across model families. We therefore introduce a controlled multimodal multiplication benchmark that factorially varies digit length, digit sparsity, representation (e.g., numerals vs. number words), and modality (text, rendered images, audio), with paired instances from a reproducible generator. We also define arithmetic load, C, as the product of the total and non-zero digit count as a compact, mechanistically motivated proxy for operation count. Across evaluations, accuracy falls sharply as C grows, often nearing zero by C > 100. Indeed, C remains predictive of performance across modalities and models, with R-squared often > 0.5, nearing the value from more complex measures of arithmetic load that count the number of intermediate arithmetic steps. A separate perception-versus-computation decomposition shows that multimodal degradation is primarily computational rather than perceptual: on matched-perception checks, models are near-perfect (> 99%) across modalities, even when multiplication accuracy drops. Beyond measuring when models fail, we ask which procedures they are predisposed to follow. We introduce a forced-completion loss probe that scores heuristic-specific reasoning prefixes--including columnar multiplication, distributive decomposition, and rounding/compensation. Here, decomposition is favored in both text and vision modalities; heuristic-specific LoRA adapters produce near-orthogonal updates yet degrade accuracy, indicating the base model maintains a well-tuned internal router.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

We obtain the multiple-parameter quantum Cram\'er-Rao bound for estimating the transverse Cartesian components of the centroid and separation of two incoherent optical point sources using an imaging system with finite spatial bandwidth. Under quite general and realistic assumptions on the point-spread function of the imaging system, and for weak source strengths, we show that the Cram\'er-Rao bounds for the x and y components of the separation are independent of the values of those components, which may be well below the conventional Rayleigh resolution limit. We also propose two linear optics-based measurement methods that approach the quantum bound for the estimation of the Cartesian components of the separation once the centroid has been located. One of the methods is an interferometric scheme that approaches the quantum bound for sub-Rayleigh separations. The other method using fiber coupling can in principle attain the bound regardless of the distance between the two sources.

Document Image Binarization is a well-known problem in Document Analysis and Computer Vision, although it is far from being solved. One of the main challenges of this task is that documents generally exhibit degradations and acquisition artifacts that can greatly vary throughout the page. Nonetheless, even when dealing with a local patch of the document, taking into account the overall appearance of a wide portion of the page can ease the prediction by enriching it with semantic information on the ink and background conditions. In this respect, approaches able to model both local and global information have been proven suitable for this task. In particular, recent applications of Vision Transformer (ViT)-based models, able to model short and long-range dependencies via the attention mechanism, have demonstrated their superiority over standard Convolution-based models, which instead struggle to model global dependencies. In this work, we propose an alternative solution based on the recently introduced Fast Fourier Convolutions, which overcomes the limitation of standard convolutions in modeling global information while requiring fewer parameters than ViTs. We validate the effectiveness of our approach via extensive experimental analysis considering different types of degradations.

Fourier PlenOctrees have shown to be an efficient representation for real-time rendering of dynamic Neural Radiance Fields (NeRF). Despite its many advantages, this method suffers from artifacts introduced by the involved compression when combining it with recent state-of-the-art techniques for training the static per-frame NeRF models. In this paper, we perform an in-depth analysis of these artifacts and leverage the resulting insights to propose an improved representation. In particular, we present a novel density encoding that adapts the Fourier-based compression to the characteristics of the transfer function used by the underlying volume rendering procedure and leads to a substantial reduction of artifacts in the dynamic model. Furthermore, we show an augmentation of the training data that relaxes the periodicity assumption of the compression. We demonstrate the effectiveness of our enhanced Fourier PlenOctrees in the scope of quantitative and qualitative evaluations on synthetic and real-world scenes.

A sample of 60,410 bona fide optical quasars with astrometric proper motions in Gaia EDR3 and spectroscopic redshifts above 0.5 in an oval 8400 square degree area of the sky is constructed. Using orthogonal Zernike functions of polar coordinates, the proper motion fields are fitted in a weighted least-squares adjustment of the entire sample and of six equal bins of sorted redshifts. The overall fit with 37 Zernike functions reveals a statistically significant pattern, which is likely to be of instrumental origin. The main feature of this pattern is a chain of peaks and dips mostly in the R.A. component with an amplitude of 25~muas yr^{-1}. This field is subtracted from each of the six analogous fits for quasars grouped by redshifts covering the range 0.5 through 7.03, with median values 0.72, 1.00, 1.25, 1.52, 1.83, 2.34. The resulting residual patterns are noisier, with formal uncertainties up to 8~muas yr^{-1} in the central part of the area. We detect a single high-confidence Zernike term for R.A. proper motion components of quasars with redshifts around 1.52 representing a general gradient of 30 muas yr^{-1} over 150degr on the sky. We do not find any small- or medium-scale systemic variations of the residual proper motion field as functions of redshift above the 2.5,sigma significance level.

Creating images from noise is image generation; reconstructing fine details from coarse inputs is super-resolution. Despite their practical differences, both can be understood as reversing information loss across scales. We introduce SKILD, a Scale-invariant K-Space Image Learning Diffusion model that unifies generation and continuous super-resolution within a single unconditional framework. Both natural images and critical physical systems exhibit scale invariance, and we leverage it to design a forward process that attenuates image content from fine to coarse scales while injecting spectrum-matched Gaussian noise, making scale an explicit coordinate of the diffusion dynamics. The same trained reverse process performs generation and continuous super-resolution by varying only the starting timestep: no task-specific architecture, no conditioning branch, no classifier-free guidance, no retraining per scale factor. Empirically, SKILD reaches FID 2.65 and Inception Score 9.63 on unconditional CIFAR-10, performs 2times--8times super-resolution on ImageNet from a single unconditional checkpoint while outperforming conditional models across perceptual metrics, and reconstructs critical Ising models whose connected four-point correlations closely track the ground truth.

We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Loève transform, and several others along with their continuous counterparts (Fourier transform, Fourier series, spherical harmonics, fractional Fourier transform) under one representation-theoretic principle: each is the eigenbasis of every covariance invariant under a specific finite or compact group, with columns constructed from the irreducible matrix elements of the group via the Peter-Weyl theorem. The unification rests on the Algebraic Diversity (AD) framework, which identifies the matched group of a covariance as the foundational object of second-order signal processing. The data-dependent KLT emerges as the trivial-matched-group limit; classical transforms emerge as the cyclic, dihedral, elementary abelian, iterated wreath, and hybrid wreath cases. Composition rules cover direct, wreath, and semidirect products. The Reed-Muller and arithmetic transforms appear as related change-of-basis transforms on the matched group of Walsh-Hadamard. A polynomial-time algorithm for matched-group discovery, the DAD-CAD relaxation cast as a generalized eigenvalue problem in double-commutator form, closes the operational loop: the matched group of any empirical covariance is discovered without expert judgment, with noise-aware variants via the commutativity residual δ and algebraic coloring index α for finite-SNR settings. The fractional Fourier transform is treated as the metaplectic SO(2) case with Hermite-Gauss matched basis, and a structural principle relates matched group size inversely to transform resolution. Modern applications (massive-MIMO, graph neural networks, transformer attention, point cloud and 3D vision, brain connectivity, single-cell genomics, quantum informatics) are sketched with their matched groups.

Remote sensing provides valuable information about objects or areas from a distance in either active (e.g., RADAR and LiDAR) or passive (e.g., multispectral and hyperspectral) modes. The quality of data acquired by remotely sensed imaging sensors (both active and passive) is often degraded by a variety of noise types and artifacts. Image restoration, which is a vibrant field of research in the remote sensing community, is the task of recovering the true unknown image from the degraded observed image. Each imaging sensor induces unique noise types and artifacts into the observed image. This fact has led to the expansion of restoration techniques in different paths according to each sensor type. This review paper brings together the advances of image restoration techniques with particular focuses on synthetic aperture radar and hyperspectral images as the most active sub-fields of image restoration in the remote sensing community. We, therefore, provide a comprehensive, discipline-specific starting point for researchers at different levels (i.e., students, researchers, and senior researchers) willing to investigate the vibrant topic of data restoration by supplying sufficient detail and references. Additionally, this review paper accompanies a toolbox to provide a platform to encourage interested students and researchers in the field to further explore the restoration techniques and fast-forward the community. The toolboxes are provided in https://github.com/ImageRestorationToolbox.

Gaussian Splatting have demonstrated remarkable novel view synthesis performance at high rendering frame rates. Optimization-based inverse rendering within complex capture scenarios remains however a challenging problem. A particular case is modelling complex surface light interactions for highly reflective scenes, which results in intricate high frequency specular radiance components. We hypothesize that such challenging settings can benefit from increased representation power. We hence propose a method that tackles this issue through a geometrically and physically grounded Gaussian Splatting borne radiance field, where normals and material properties are spatially variable in the primitive's local space. Using per-primitive texture maps for this purpose, we also propose to harness the GPU hardware to accelerate rendering at test time via unified material texture atlas. Code will be available at https://github.com/maeyounes/TextureSplat

We demonstrate a new computational illumination technique that achieves large space-bandwidth-time product, for quantitative phase imaging of unstained live samples in vitro. Microscope lenses can have either large field of view (FOV) or high resolution, not both. Fourier ptychographic microscopy (FPM) is a new computational imaging technique that circumvents this limit by fusing information from multiple images taken with different illumination angles. The result is a gigapixel-scale image having both wide FOV and high resolution, i.e. large space-bandwidth product (SBP). FPM has enormous potential for revolutionizing microscopy and has already found application in digital pathology. However, it suffers from long acquisition times (on the order of minutes), limiting throughput. Faster capture times would not only improve imaging speed, but also allow studies of live samples, where motion artifacts degrade results. In contrast to fixed (e.g. pathology) slides, live samples are continuously evolving at various spatial and temporal scales. Here, we present a new source coding scheme, along with real-time hardware control, to achieve 0.8 NA resolution across a 4x FOV with sub-second capture times. We propose an improved algorithm and new initialization scheme, which allow robust phase reconstruction over long time-lapse experiments. We present the first FPM results for both growing and confluent in vitro cell cultures, capturing videos of subcellular dynamical phenomena in popular cell lines undergoing division and migration. Our method opens up FPM to applications with live samples, for observing rare events in both space and time.

In recent years, the neural radiance field (NeRF) model has gained popularity due to its ability to recover complex 3D scenes. Following its success, many approaches proposed different NeRF representations in order to further improve both runtime and performance. One such example is Triplane, in which NeRF is represented using three 2D feature planes. This enables easily using existing 2D neural networks in this framework, e.g., to generate the three planes. Despite its advantage, the triplane representation lagged behind in its 3D recovery quality compared to NeRF solutions. In this work, we propose TriNeRFLet, a 2D wavelet-based multiscale triplane representation for NeRF, which closes the 3D recovery performance gap and is competitive with current state-of-the-art methods. Building upon the triplane framework, we also propose a novel super-resolution (SR) technique that combines a diffusion model with TriNeRFLet for improving NeRF resolution.

We propose a learning-based method to recover normals, specularity, and roughness from a single diffuse image of a material, using microgeometry appearance as our primary cue. Previous methods that work on single images tend to produce over-smooth outputs with artifacts, operate at limited resolution, or train one model per class with little room for generalization. Previous methods that work on single images tend to produce over-smooth outputs with artifacts, operate at limited resolution, or train one model per class with little room for generalization. In contrast, in this work, we propose a novel capture approach that leverages a generative network with attention and a U-Net discriminator, which shows outstanding performance integrating global information at reduced computational complexity. We showcase the performance of our method with a real dataset of digitized textile materials and show that a commodity flatbed scanner can produce the type of diffuse illumination required as input to our method. Additionally, because the problem might be illposed -more than a single diffuse image might be needed to disambiguate the specular reflection- or because the training dataset is not representative enough of the real distribution, we propose a novel framework to quantify the model's confidence about its prediction at test time. Our method is the first one to deal with the problem of modeling uncertainty in material digitization, increasing the trustworthiness of the process and enabling more intelligent strategies for dataset creation, as we demonstrate with an active learning experiment.

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.

Capturing highly appreciated star field images is extremely challenging due to light pollution, the requirements of specialized hardware, and the high level of photographic skills needed. Deep learning-based techniques have achieved remarkable results in low-light image enhancement (LLIE) but have not been widely applied to star field image enhancement due to the lack of training data. To address this problem, we construct the first Star Field Image Enhancement Benchmark (SFIEB) that contains 355 real-shot and 854 semi-synthetic star field images, all having the corresponding reference images. Using the presented dataset, we propose the first star field image enhancement approach, namely StarDiffusion, based on conditional denoising diffusion probabilistic models (DDPM). We introduce dynamic stochastic corruptions to the inputs of conditional DDPM to improve the performance and generalization of the network on our small-scale dataset. Experiments show promising results of our method, which outperforms state-of-the-art low-light image enhancement algorithms. The dataset and codes will be open-sourced.

Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive, and sometimes even impossible to implement. We study a challenging problem called self-calibration, i.e., the task of designing an algorithm for devices so that the algorithm is able to perform calibration automatically. More precisely, we consider the setup y = A(d) x + epsilon where only partial information about the sensing matrix A(d) is known and where A(d) linearly depends on d. The goal is to estimate the calibration parameter d (resolve the uncertainty in the sensing process) and the signal/object of interests x simultaneously. For three different models of practical relevance, we show how such a bilinear inverse problem, including blind deconvolution as an important example, can be solved via a simple linear least squares approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus potentially allowing for real-time deployment. We also present a variation of the least squares approach, which leads to a~spectral method, where the solution to the bilinear inverse problem can be found by computing the singular vector associated with the smallest singular value of a certain matrix derived from the bilinear system. Explicit theoretical guarantees and stability theory are derived for both techniques; and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

Detecting oscillations in solar and stellar time series is complicated by non-stationary red noise and evolving background emission. Methods based on detrending and AR(1)-based wavelet analysis can introduce spurious periodicities and do not adequately describe time-dependent backgrounds. We develop a Bayesian approach that combines the continuous wavelet transform with MCMC sampling to infer a time-dependent background spectrum. The background is represented by a power-law plus white-noise component, with parameters allowed to vary smoothly in time, so that significance levels can be evaluated locally without explicit detrending. Tests with synthetic data show that injected oscillations are recovered reliably, while false detections are suppressed in pure-noise cases. Using a frequency-domain signal-to-noise ratio (S/N), we find that oscillations can be identified robustly when the S/N is greater than or equal to 2 under mixed noise conditions. The detectable period range is limited by wavelet resolution, from about 3-4 sampling intervals up to roughly one-quarter of the total duration. Application to GOES soft X-ray flare observations shows that the method isolates quasi-periodic oscillations with improved temporal localization compared to standard wavelet and Fourier-based approaches. Meanwhile, this behavior is consistent across a range of noise conditions and signal morphologies.

We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information theory and estimation theory, which links the log-probability of a signal with the errors of an optimal denoiser, applied to noisy observations of the signal. In particular, the IEM between a pair of signals is obtained by comparing their denoising error vectors over a range of noise amplitudes. Geometrically, this amounts to comparing the score vector fields of the blurred density around the signals over a range of blur levels. We prove that the IEM is a valid global distance metric and derive a closed-form expression for its local second-order approximation, which yields a Riemannian metric. For Gaussian-distributed signals, the IEM coincides with the Mahalanobis distance. But for more complex distributions, it adapts, both locally and globally, to the geometry of the distribution. In practice, the IEM can be computed using a learned denoiser (analogous to generative diffusion models) and solving a one-dimensional integral. To demonstrate the value of our framework, we learn an IEM on the ImageNet database. Experiments show that this IEM is competitive with or outperforms state-of-the-art supervised image quality metrics in predicting human perceptual judgments.

This paper introduces MVDiffusion, a simple yet effective multi-view image generation method for scenarios where pixel-to-pixel correspondences are available, such as perspective crops from panorama or multi-view images given geometry (depth maps and poses). Unlike prior models that rely on iterative image warping and inpainting, MVDiffusion concurrently generates all images with a global awareness, encompassing high resolution and rich content, effectively addressing the error accumulation prevalent in preceding models. MVDiffusion specifically incorporates a correspondence-aware attention mechanism, enabling effective cross-view interaction. This mechanism underpins three pivotal modules: 1) a generation module that produces low-resolution images while maintaining global correspondence, 2) an interpolation module that densifies spatial coverage between images, and 3) a super-resolution module that upscales into high-resolution outputs. In terms of panoramic imagery, MVDiffusion can generate high-resolution photorealistic images up to 1024times1024 pixels. For geometry-conditioned multi-view image generation, MVDiffusion demonstrates the first method capable of generating a textured map of a scene mesh. The project page is at https://mvdiffusion.github.io.

Distinction of OFDM signals from single carrier signals is highly important for adaptive receiver algorithms and signal identification applications. OFDM signals exhibit Gaussian characteristics in time domain and fourth order cumulants of Gaussian distributed signals vanish in contrary to the cumulants of other signals. Thus fourth order cumulants can be utilized for OFDM signal identification. In this paper, first, formulations of the estimates of the fourth order cumulants for OFDM signals are provided. Then it is shown these estimates are affected significantly from the wireless channel impairments, frequency offset, phase offset and sampling mismatch. To overcome these problems, a general chi-square constant false alarm rate Gaussianity test which employs estimates of cumulants and their covariances is adapted to the specific case of wireless OFDM signals. Estimation of the covariance matrix of the fourth order cumulants are greatly simplified peculiar to the OFDM signals. A measurement setup is developed to analyze the performance of the identification method and for comparison purposes. A parametric measurement analysis is provided depending on modulation order, signal to noise ratio, number of symbols, and degree of freedom of the underlying test. The proposed method outperforms statistical tests which are based on fixed thresholds or empirical values, while a priori information requirement and complexity of the proposed method are lower than the coherent identification techniques.

Photo-realistic image restoration algorithms are typically evaluated by distortion measures (e.g., PSNR, SSIM) and by perceptual quality measures (e.g., FID, NIQE), where the desire is to attain the lowest possible distortion without compromising on perceptual quality. To achieve this goal, current methods typically attempt to sample from the posterior distribution, or to optimize a weighted sum of a distortion loss (e.g., MSE) and a perceptual quality loss (e.g., GAN). Unlike previous works, this paper is concerned specifically with the optimal estimator that minimizes the MSE under a constraint of perfect perceptual index, namely where the distribution of the reconstructed images is equal to that of the ground-truth ones. A recent theoretical result shows that such an estimator can be constructed by optimally transporting the posterior mean prediction (MMSE estimate) to the distribution of the ground-truth images. Inspired by this result, we introduce Posterior-Mean Rectified Flow (PMRF), a simple yet highly effective algorithm that approximates this optimal estimator. In particular, PMRF first predicts the posterior mean, and then transports the result to a high-quality image using a rectified flow model that approximates the desired optimal transport map. We investigate the theoretical utility of PMRF and demonstrate that it consistently outperforms previous methods on a variety of image restoration tasks.

Image interpolation based on diffusion models is promising in creating fresh and interesting images. Advanced interpolation methods mainly focus on spherical linear interpolation, where images are encoded into the noise space and then interpolated for denoising to images. However, existing methods face challenges in effectively interpolating natural images (not generated by diffusion models), thereby restricting their practical applicability. Our experimental investigations reveal that these challenges stem from the invalidity of the encoding noise, which may no longer obey the expected noise distribution, e.g., a normal distribution. To address these challenges, we propose a novel approach to correct noise for image interpolation, NoiseDiffusion. Specifically, NoiseDiffusion approaches the invalid noise to the expected distribution by introducing subtle Gaussian noise and introduces a constraint to suppress noise with extreme values. In this context, promoting noise validity contributes to mitigating image artifacts, but the constraint and introduced exogenous noise typically lead to a reduction in signal-to-noise ratio, i.e., loss of original image information. Hence, NoiseDiffusion performs interpolation within the noisy image space and injects raw images into these noisy counterparts to address the challenge of information loss. Consequently, NoiseDiffusion enables us to interpolate natural images without causing artifacts or information loss, thus achieving the best interpolation results.

Operational phase unwrapping is the primary computational bottleneck in InSAR-based volcanic and seismic monitoring. We challenge the industry trend of adopting high-complexity computer vision architectures, such as attention mechanisms, without validating their suitability for physics-constrained geophysical regression. We present the first large-scale architectural ablation study on a global LiCSAR benchmark (20 frames, 39,724 patches, 651M pixels). Our results reveal a significant "complexity penalty": a vanilla U-Net (7.76M parameters) achieves R^2=0.834 and RMSE = 1.01 cm, outperforming 11.37M-parameter attention-based models by 34% in R^2 and 51% in RMSE. Power Spectral Density (PSD) analysis provides the physical justification: while attention excels at capturing sharp semantic edges in natural images, it injects unphysical high-frequency artifacts (>0.3 cycles/pixel) into geophysical fields, violating the fundamental smoothness constraints of elastic surface deformation. With a 2.92ms inference latency (a 2.5times speedup), the vanilla U-Net is the only candidate to comfortably meet the sub-100ms requirement for operational early-warning systems. This work bridges the "publication-to-practice" gap by proving that convolutional locality outperforms modern complexity for smooth-field regression, advocating for physics-informed simplicity in ML4RS. Code available at https://github.com/prabhjotschugh/When-Less-is-More-InSAR-Phase-Unwrapping

We present a new way to merge any two point distribution approaches using distance fields. Our new process allows us to produce digital stippling that fills areas with stipple dots without visual artifacts as well as includes clear linear features without fussiness. Our merging thus benefits from past work that can optimize for either goal individually, yet typically by sacrificing the other. The new possibility of combining any two distributions using different distance field functions and their parameters also allows us to produce a vast range of stippling styles, which we demonstrate as well.

Recent advances in autoregressive (AR) models with continuous tokens for image generation show promising results by eliminating the need for discrete tokenization. However, these models face efficiency challenges due to their sequential token generation nature and reliance on computationally intensive diffusion-based sampling. We present ECAR (Efficient Continuous Auto-Regressive Image Generation via Multistage Modeling), an approach that addresses these limitations through two intertwined innovations: (1) a stage-wise continuous token generation strategy that reduces computational complexity and provides progressively refined token maps as hierarchical conditions, and (2) a multistage flow-based distribution modeling method that transforms only partial-denoised distributions at each stage comparing to complete denoising in normal diffusion models. Holistically, ECAR operates by generating tokens at increasing resolutions while simultaneously denoising the image at each stage. This design not only reduces token-to-image transformation cost by a factor of the stage number but also enables parallel processing at the token level. Our approach not only enhances computational efficiency but also aligns naturally with image generation principles by operating in continuous token space and following a hierarchical generation process from coarse to fine details. Experimental results demonstrate that ECAR achieves comparable image quality to DiT Peebles & Xie [2023] while requiring 10times FLOPs reduction and 5times speedup to generate a 256times256 image.

We consider the convergence of the ESD for non-Hermitian random band matrices with independent entries to the circular law, which is the uniform measure on the unit disk in the center of the complex plane. We assume that the bandwidth of the matrix scales like n^γ for some γin(0,1], where n is the matrix size, and the variance profile of the matrix is only assumed to be doubly stochastic with no additional assumption on its specific mixing properties. We prove that the circular law limit holds either (1) when γ>5{6} and the entries are independent Gaussians, (2) or when γ>8{9} and the entries are independent subgaussian random variables. This new threshold improves the previous threshold γ>32{33} which was only proven for block band matrices and periodic band matrices. After the initial version of this paper, the author further extended the range of circular law for much smaller values of γ in 2508.18143 and 2511.01744 when the variance profile has specific mixing properties, but not for an arbitrary doubly stochastic variance profile. Thus the main contribution of this paper is the circular law for a genuine power law bandwidth for any doubly stochastic variance profile. We also prove an extended form of product circular law with a growing number of matrices. Weak delocalization estimates on eigenvectors are also derived. The new technical input is new polynomial lower bounds on some intermediate small singular values, and this estimate does not depend on the specific structure of the variance profile beyond the fact that it is doubly stochastic.

3D reconstruction from unconstrained image collections presents substantial challenges due to varying appearances and transient occlusions. In this paper, we introduce Micro-macro Wavelet-based Gaussian Splatting (MW-GS), a novel approach designed to enhance 3D reconstruction by disentangling scene representations into global, refined, and intrinsic components. The proposed method features two key innovations: Micro-macro Projection, which allows Gaussian points to capture details from feature maps across multiple scales with enhanced diversity; and Wavelet-based Sampling, which leverages frequency domain information to refine feature representations and significantly improve the modeling of scene appearances. Additionally, we incorporate a Hierarchical Residual Fusion Network to seamlessly integrate these features. Extensive experiments demonstrate that MW-GS delivers state-of-the-art rendering performance, surpassing existing methods.

Advancements in 3D Gaussian Splatting have significantly accelerated 3D reconstruction and generation. However, it may require a large number of Gaussians, which creates a substantial memory footprint. This paper introduces GES (Generalized Exponential Splatting), a novel representation that employs Generalized Exponential Function (GEF) to model 3D scenes, requiring far fewer particles to represent a scene and thus significantly outperforming Gaussian Splatting methods in efficiency with a plug-and-play replacement ability for Gaussian-based utilities. GES is validated theoretically and empirically in both principled 1D setup and realistic 3D scenes. It is shown to represent signals with sharp edges more accurately, which are typically challenging for Gaussians due to their inherent low-pass characteristics. Our empirical analysis demonstrates that GEF outperforms Gaussians in fitting natural-occurring signals (e.g. squares, triangles, and parabolic signals), thereby reducing the need for extensive splitting operations that increase the memory footprint of Gaussian Splatting. With the aid of a frequency-modulated loss, GES achieves competitive performance in novel-view synthesis benchmarks while requiring less than half the memory storage of Gaussian Splatting and increasing the rendering speed by up to 39%. The code is available on the project website https://abdullahamdi.com/ges .

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number M of open channels the probability density {cal P}(I) for the single-point intensity I decays as a power law for large intensities: {cal P}(I)sim I^{-(M+2)}, provided there is no internal losses. This behaviour is in marked difference with the Rayleigh law {cal P}(I)sim exp(-I/I) which turns out to be valid only in the limit Mto infty. We also find the joint probability density of intensities I_1, ldots, I_L in L>1 observation points, and then extract the corresponding statistics for the maximal intensity in the observation pattern. For Lto infty the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions.

Hyperspectral image (HSI) plays a vital role in various fields such as agriculture and environmental monitoring. However, due to the expensive acquisition cost, the number of hyperspectral images is limited, degenerating the performance of downstream tasks. Although some recent studies have attempted to employ diffusion models to synthesize HSIs, they still struggle with the scarcity of HSIs, affecting the reliability and diversity of the generated images. Some studies propose to incorporate multi-modal data to enhance spatial diversity, but the spectral fidelity cannot be ensured. In addition, existing HSI synthesis models are typically uncontrollable or only support single-condition control, limiting their ability to generate accurate and reliable HSIs. To alleviate these issues, we propose HSIGene, a novel HSI generation foundation model which is based on latent diffusion and supports multi-condition control, allowing for more precise and reliable HSI generation. To enhance the spatial diversity of the training data while preserving spectral fidelity, we propose a new data augmentation method based on spatial super-resolution, in which HSIs are upscaled first, and thus abundant training patches could be obtained by cropping the high-resolution HSIs. In addition, to improve the perceptual quality of the augmented data, we introduce a novel two-stage HSI super-resolution framework, which first applies RGB bands super-resolution and then utilizes our proposed Rectangular Guided Attention Network (RGAN) for guided HSI super-resolution. Experiments demonstrate that the proposed model is capable of generating a vast quantity of realistic HSIs for downstream tasks such as denoising and super-resolution. The code and models are available at https://github.com/LiPang/HSIGene.

Multi-spectral imagery plays a crucial role in diverse Remote Sensing applications including land-use classification, environmental monitoring and urban planning. These images are widely adopted because their additional spectral bands correlate strongly with physical materials on the ground, such as ice, water, and vegetation. This allows for more accurate identification, and their public availability from missions, such as Sentinel-2 and Landsat, only adds to their value. Currently, the automatic analysis of such data is predominantly managed through machine learning models specifically trained for multi-spectral input, which are costly to train and support. Furthermore, although providing a lot of utility for Remote Sensing, such additional inputs cannot be used with powerful generalist large multimodal models, which are capable of solving many visual problems, but are not able to understand specialized multi-spectral signals. To address this, we propose a training-free approach which introduces new multi-spectral data in a Zero-Shot-only mode, as inputs to generalist multimodal models, trained on RGB-only inputs. Our approach leverages the multimodal models' understanding of the visual space, and proposes to adapt to inputs to that space, and to inject domain-specific information as instructions into the model. We exemplify this idea with the Gemini2.5 model and observe strong Zero-Shot performance gains of the approach on popular Remote Sensing benchmarks for land cover and land use classification and demonstrate the easy adaptability of Gemini2.5 to new inputs. These results highlight the potential for geospatial professionals, working with non-standard specialized inputs, to easily leverage powerful multimodal models, such as Gemini2.5, to accelerate their work, benefiting from their rich reasoning and contextual capabilities, grounded in the specialized sensor data.

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

Recent advancements in Mamba have shown promising results in image restoration. These methods typically flatten 2D images into multiple distinct 1D sequences along rows and columns, process each sequence independently using selective scan operation, and recombine them to form the outputs. However, such a paradigm overlooks two vital aspects: i) the local relationships and spatial continuity inherent in natural images, and ii) the discrepancies among sequences unfolded through totally different ways. To overcome the drawbacks, we explore two problems in Mamba-based restoration methods: i) how to design a scanning strategy preserving both locality and continuity while facilitating restoration, and ii) how to aggregate the distinct sequences unfolded in totally different ways. To address these problems, we propose a novel Mamba-based Image Restoration model (MaIR), which consists of Nested S-shaped Scanning strategy (NSS) and Sequence Shuffle Attention block (SSA). Specifically, NSS preserves locality and continuity of the input images through the stripe-based scanning region and the S-shaped scanning path, respectively. SSA aggregates sequences through calculating attention weights within the corresponding channels of different sequences. Thanks to NSS and SSA, MaIR surpasses 40 baselines across 14 challenging datasets, achieving state-of-the-art performance on the tasks of image super-resolution, denoising, deblurring and dehazing. The code is available at https://github.com/XLearning-SCU/2025-CVPR-MaIR.

Denoising diffusion models (DDMs) have led to staggering performance leaps in image generation, editing and restoration. However, existing DDMs use very large datasets for training. Here, we introduce a framework for training a DDM on a single image. Our method, which we coin SinDDM, learns the internal statistics of the training image by using a multi-scale diffusion process. To drive the reverse diffusion process, we use a fully-convolutional light-weight denoiser, which is conditioned on both the noise level and the scale. This architecture allows generating samples of arbitrary dimensions, in a coarse-to-fine manner. As we illustrate, SinDDM generates diverse high-quality samples, and is applicable in a wide array of tasks, including style transfer and harmonization. Furthermore, it can be easily guided by external supervision. Particularly, we demonstrate text-guided generation from a single image using a pre-trained CLIP model.

Earth Observation (EO) data are increasingly used in policy analysis by enabling granular estimation of treatment effects. However, a challenge in EO-based causal inference lies in balancing the trade-off between capturing fine-grained individual heterogeneity and broader contextual information. This paper introduces Multi-scale Concatenation, a family of composable procedures that transform arbitrary single-scale CATE estimation algorithms into multi-scale algorithms. We benchmark the performance of Multi-scale Concatenation on a CATE estimation pipeline combining Vision Transformer (ViT) models fine-tuned on satellite images to encode images of different scales with Causal Forests to obtain the final CATE estimate. We first perform simulation studies, showing how a multi-scale approach captures multi-level dynamics that single-scale ViT models fail to capture. We then apply the multi-scale method to two randomized controlled trials (RCTs) conducted in Peru and Uganda using Landsat satellite imagery. In the RCT analysis, the Rank Average Treatment Effect Ratio (RATE Ratio) measure is employed to assess performance without ground truth individual treatment effects. Results indicate that Multi-scale Concatenation improves the performance of deep learning models in EO-based CATE estimation without the complexity of designing new multi-scale architectures for a specific use case.

Generative models trained on extensive high-quality datasets effectively capture the structural and statistical properties of clean images, rendering them powerful priors for transforming degraded features into clean ones in image restoration. VAR, a novel image generative paradigm, surpasses diffusion models in generation quality by applying a next-scale prediction approach. It progressively captures both global structures and fine-grained details through the autoregressive process, consistent with the multi-scale restoration principle widely acknowledged in the restoration community. Furthermore, we observe that during the image reconstruction process utilizing VAR, scale predictions automatically modulate the input, facilitating the alignment of representations at subsequent scales with the distribution of clean images. To harness VAR's adaptive distribution alignment capability in image restoration tasks, we formulate the multi-scale latent representations within VAR as the restoration prior, thus advancing our delicately designed VarFormer framework. The strategic application of these priors enables our VarFormer to achieve remarkable generalization on unseen tasks while also reducing training computational costs. Extensive experiments underscores that our VarFormer outperforms existing multi-task image restoration methods across various restoration tasks.

Image denoising is a fundamental challenge in computer vision, with applications in photography and medical imaging. While deep learning-based methods have shown remarkable success, their reliance on specific noise distributions limits generalization to unseen noise types and levels. Existing approaches attempt to address this with extensive training data and high computational resources but they still suffer from overfitting. To address these issues, we conduct image denoising by utilizing dynamically generated kernels via efficient operations. This approach helps prevent overfitting and improves resilience to unseen noise. Specifically, our method leverages a Feature Extraction Module for robust noise-invariant features, Global Statistics and Local Correlation Modules to capture comprehensive noise characteristics and structural correlations. The Kernel Prediction Module then employs these cues to produce pixel-wise varying kernels adapted to local structures, which are then applied iteratively for denoising. This ensures both efficiency and superior restoration quality. Despite being trained on single-level Gaussian noise, our compact model (~ 0.04 M) excels across diverse noise types and levels, demonstrating the promise of iterative dynamic filtering for practical image denoising.

In this paper, we present a Hybrid Spectral Denoising Transformer (HSDT) for hyperspectral image denoising. Challenges in adapting transformer for HSI arise from the capabilities to tackle existing limitations of CNN-based methods in capturing the global and local spatial-spectral correlations while maintaining efficiency and flexibility. To address these issues, we introduce a hybrid approach that combines the advantages of both models with a Spatial-Spectral Separable Convolution (S3Conv), Guided Spectral Self-Attention (GSSA), and Self-Modulated Feed-Forward Network (SM-FFN). Our S3Conv works as a lightweight alternative to 3D convolution, which extracts more spatial-spectral correlated features while keeping the flexibility to tackle HSIs with an arbitrary number of bands. These features are then adaptively processed by GSSA which per-forms 3D self-attention across the spectral bands, guided by a set of learnable queries that encode the spectral signatures. This not only enriches our model with powerful capabilities for identifying global spectral correlations but also maintains linear complexity. Moreover, our SM-FFN proposes the self-modulation that intensifies the activations of more informative regions, which further strengthens the aggregated features. Extensive experiments are conducted on various datasets under both simulated and real-world noise, and it shows that our HSDT significantly outperforms the existing state-of-the-art methods while maintaining low computational overhead. Code is at https: //github.com/Zeqiang-Lai/HSDT.

Neural Radiance Fields (NeRF) is a revolutionary approach for rendering scenes by sampling a single ray per pixel and it has demonstrated impressive capabilities in novel-view synthesis from static scene images. However, in practice, we usually need to recover NeRF from unconstrained image collections, which poses two challenges: 1) the images often have dynamic changes in appearance because of different capturing time and camera settings; 2) the images may contain transient objects such as humans and cars, leading to occlusion and ghosting artifacts. Conventional approaches seek to address these challenges by locally utilizing a single ray to synthesize a color of a pixel. In contrast, humans typically perceive appearance and objects by globally utilizing information across multiple pixels. To mimic the perception process of humans, in this paper, we propose Cross-Ray NeRF (CR-NeRF) that leverages interactive information across multiple rays to synthesize occlusion-free novel views with the same appearances as the images. Specifically, to model varying appearances, we first propose to represent multiple rays with a novel cross-ray feature and then recover the appearance by fusing global statistics, i.e., feature covariance of the rays and the image appearance. Moreover, to avoid occlusion introduced by transient objects, we propose a transient objects handler and introduce a grid sampling strategy for masking out the transient objects. We theoretically find that leveraging correlation across multiple rays promotes capturing more global information. Moreover, extensive experimental results on large real-world datasets verify the effectiveness of CR-NeRF.

This study introduces a modular framework for spatial image processing, integrating grayscale quantization, color and brightness enhancement, image sharpening, bidirectional transformation pipelines, and geometric feature extraction. A stepwise intensity transformation quantizes grayscale images into eight discrete levels, producing a posterization effect that simplifies representation while preserving structural detail. Color enhancement is achieved via histogram equalization in both RGB and YCrCb color spaces, with the latter improving contrast while maintaining chrominance fidelity. Brightness adjustment is implemented through HSV value-channel manipulation, and image sharpening is performed using a 3 * 3 convolution kernel to enhance high-frequency details. A bidirectional transformation pipeline that integrates unsharp masking, gamma correction, and noise amplification achieved accuracy levels of 76.10% and 74.80% for the forward and reverse processes, respectively. Geometric feature extraction employed Canny edge detection, Hough-based line estimation (e.g., 51.50{\deg} for billiard cue alignment), Harris corner detection, and morphological window localization. Cue isolation further yielded 81.87\% similarity against ground truth images. Experimental evaluation across diverse datasets demonstrates robust and deterministic performance, highlighting its potential for real-time image analysis and computer vision.

Pansharpening aims to combine a high-resolution panchromatic (PAN) image with a low-resolution multispectral (LRMS) image to produce a high-resolution multispectral (HRMS) image. Although pansharpening in the frequency domain offers clear advantages, most existing methods either continue to operate solely in the spatial domain or fail to fully exploit the benefits of the frequency domain. To address this issue, we innovatively propose Multi-Frequency Fusion Attention (MFFA), which leverages wavelet transforms to cleanly separate frequencies and enable lossless reconstruction across different frequency domains. Then, we generate Frequency-Query, Spatial-Key, and Fusion-Value based on the physical meanings represented by different features, which enables a more effective capture of specific information in the frequency domain. Additionally, we focus on the preservation of frequency features across different operations. On a broader level, our network employs a wavelet pyramid to progressively fuse information across multiple scales. Compared to previous frequency domain approaches, our network better prevents confusion and loss of different frequency features during the fusion process. Quantitative and qualitative experiments on multiple datasets demonstrate that our method outperforms existing approaches and shows significant generalization capabilities for real-world scenarios.

Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In this paper, we show that current diffusion models actually have an expressive bottleneck in backward denoising and some assumption made by existing theoretical guarantees is too strong. Based on this finding, we prove that diffusion models have unbounded errors in both local and global denoising. In light of our theoretical studies, we introduce soft mixture denoising (SMD), an expressive and efficient model for backward denoising. SMD not only permits diffusion models to well approximate any Gaussian mixture distributions in theory, but also is simple and efficient for implementation. Our experiments on multiple image datasets show that SMD significantly improves different types of diffusion models (e.g., DDPM), espeically in the situation of few backward iterations.

The k-means++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the k-means clustering problem where the goal is to cluster a dataset X subset R ^d into k clusters. The popularity of this algorithm is due to its simplicity and provable guarantee of being O(log k) competitive with the optimal solution in expectation. However, its running time is O(|X|kd), making it expensive for large datasets. In this work, we present a simple and effective rejection sampling based approach for speeding up k-means++. Our first method runs in time O(nnz (X) + beta k^2d) while still being O(log k ) competitive in expectation. Here, beta is a parameter which is the ratio of the variance of the dataset to the optimal k-means cost in expectation and O hides logarithmic factors in k and |X|. Our second method presents a new trade-off between computational cost and solution quality. It incurs an additional scale-invariant factor of k^{-Omega( m/beta)} Var (X) in addition to the O(log k) guarantee of k-means++ improving upon a result of (Bachem et al, 2016a) who get an additional factor of m^{-1}Var(X) while still running in time O(nnz(X) + mk^2d). We perform extensive empirical evaluations to validate our theoretical results and to show the effectiveness of our approach on real datasets.

We introduce a novel method for measuring properties of periodic phenomena with an event camera, a device asynchronously reporting brightness changes at independently operating pixels. The approach assumes that for fast periodic phenomena, in any spatial window where it occurs, a very similar set of events is generated at the time difference corresponding to the frequency of the motion. To estimate the frequency, we compute correlations of spatio-temporal windows in the event space. The period is calculated from the time differences between the peaks of the correlation responses. The method is contactless, eliminating the need for markers, and does not need distinguishable landmarks. We evaluate the proposed method on three instances of periodic phenomena: (i) light flashes, (ii) vibration, and (iii) rotational speed. In all experiments, our method achieves a relative error lower than 0.04%, which is within the error margin of ground truth measurements.

Factories, museums and surveyors photograph the same space months apart and need to know which objects changed. When each visit is reconstructed with 3D Gaussian Splatting (3DGS), a direct comparison of the two reconstructions does not answer this. Training is stochastic, so two reconstructions of an unchanged space never coincide, and the second visit is often a quick re-scan with far fewer photographs. We propose GS-Pool, which takes two independently reconstructed Gaussian fields of the same space and returns the changed objects in each, together with their masks. SAM2 masks of each visit's photographs are lifted onto the Gaussians that render them and merged into an object pool, so every decision is taken once per object in 3D. We introduce a photographic carrier, the 3DGS training loss of each input reconstruction against the other visit's photographs, backpropagated to the Gaussians that rendered each pixel. We combine it with GS-Diff's geometry and colour terms and our distilled DINOv3 features. This evidence is compared with that of the objects present in both visits, which sets a change threshold for each scene. On PASLCD, GS-Pool reaches mIoU/F1 scores of 0.751/0.846 against 0.644/0.758 for GS-Diff, the strongest prior method, a gain of 17%/12%. Its mIoU is also 36%, 40% and 57% above that of O-SCD, PlenoCI and MV-3DCD, and it reaches 0.855 mIoU on CL-Splats, 33% above MV-3DCD. Each changed object is returned as a set of Gaussians with the evidence behind its decision, which an inspector can review in 3D.

Hyperspectral image denoising is unique for the highly similar and correlated spectral information that should be properly considered. However, existing methods show limitations in exploring the spectral correlations across different bands and feature interactions within each band. Besides, the low- and high-level features usually exhibit different importance for different spatial-spectral regions, which is not fully explored for current algorithms as well. In this paper, we present a Mixed Attention Network (MAN) that simultaneously considers the inter- and intra-spectral correlations as well as the interactions between low- and high-level spatial-spectral meaningful features. Specifically, we introduce a multi-head recurrent spectral attention that efficiently integrates the inter-spectral features across all the spectral bands. These features are further enhanced with a progressive spectral channel attention by exploring the intra-spectral relationships. Moreover, we propose an attentive skip-connection that adaptively controls the proportion of the low- and high-level spatial-spectral features from the encoder and decoder to better enhance the aggregated features. Extensive experiments show that our MAN outperforms existing state-of-the-art methods on simulated and real noise settings while maintaining a low cost of parameters and running time.

In this paper, we introduce SP^3, a novel Plug-and-Play algorithm that accelerates maximum a posteriori image restoration by replacing denoisers with Spherical Encoders (SE) as generative priors. SP^3 approximates the intractable proximal prior step by utilizing the SE tightly structured latent space as a robust projection onto the natural image manifold. Alternating this projection with a closed-form data-consistency step, via Half-Quadratic Splitting, achieves stable convergence without requiring gradient computation during inference. This unique formulation unlocks "anytime" restoration capabilities, producing sharp, plausible images from the first iteration. Evaluations across a variety of image restoration tasks demonstrate that SP^3 achieves perceptual quality comparable to state-of-the-art zero-shot diffusion and flow methods while being 3-630times faster.

Differentiable volumetric rendering-based methods made significant progress in novel view synthesis. On one hand, innovative methods have replaced the Neural Radiance Fields (NeRF) network with locally parameterized structures, enabling high-quality renderings in a reasonable time. On the other hand, approaches have used differentiable splatting instead of NeRF's ray casting to optimize radiance fields rapidly using Gaussian kernels, allowing for fine adaptation to the scene. However, differentiable ray casting of irregularly spaced kernels has been scarcely explored, while splatting, despite enabling fast rendering times, is susceptible to clearly visible artifacts. Our work closes this gap by providing a physically consistent formulation of the emitted radiance c and density {\sigma}, decomposed with Gaussian functions associated with Spherical Gaussians/Harmonics for all-frequency colorimetric representation. We also introduce a method enabling differentiable ray casting of irregularly distributed Gaussians using an algorithm that integrates radiance fields slab by slab and leverages a BVH structure. This allows our approach to finely adapt to the scene while avoiding splatting artifacts. As a result, we achieve superior rendering quality compared to the state-of-the-art while maintaining reasonable training times and achieving inference speeds of 25 FPS on the Blender dataset. Project page with videos and code: https://raygauss.github.io/

Image Super-Resolution is a fundamental problem in computer vision with broad applications spacing from medical imaging to satellite analysis. The ability to reconstruct high-resolution images from low-resolution inputs is crucial for enhancing downstream tasks such as object detection and segmentation. While deep learning has significantly advanced SR, achieving high-quality reconstructions with fine-grained details and realistic textures remains challenging, particularly at high upscaling factors. Recent approaches leveraging diffusion models have demonstrated promising results, yet they often struggle to balance perceptual quality with structural fidelity. In this work, we introduce ResQu a novel SR framework that integrates a quaternion wavelet preprocessing framework with latent diffusion models, incorporating a new quaternion wavelet- and time-aware encoder. Unlike prior methods that simply apply wavelet transforms within diffusion models, our approach enhances the conditioning process by exploiting quaternion wavelet embeddings, which are dynamically integrated at different stages of denoising. Furthermore, we also leverage the generative priors of foundation models such as Stable Diffusion. Extensive experiments on domain-specific datasets demonstrate that our method achieves outstanding SR results, outperforming in many cases existing approaches in perceptual quality and standard evaluation metrics. The code will be available after the revision process.

Classical CUSUM relies on the log-likelihood ratio of the underlying distributions, which cannot generally be computed from finite pre- and post-change samples alone. We propose diffusion-integrated score CUSUM (DI-SCUSUM), a training-free detector. We add Gaussian noise to the samples to form two smooth density estimates and calculate their Hyvärinen scores exactly, without training a score network. For each incoming observation, we sample a diffusion time, perturb the observation, and use the importance-weighted score difference as an increment in the DI-SCUSUM recursion. Under the assumption that observations follow the fixed empirical distributions, the post-change mean increment is proportional to the Kullback-Leibler (KL) divergence from the smoothed post-change to the smoothed pre-change empirical distribution. We establish exponential false-alarm scaling and a first-order delay bound that, for a fixed threshold and increment scaling, is inversely proportional to the KL divergence. In the calibrated anisotropic Gaussian simulation, DI-SCUSUM nearly matches likelihood-ratio CUSUM and reduces the measured detection delay by about 91% relative to score-based CUSUM. On MNIST and Oxford-IIIT Pet, DI-SCUSUM also has lower empirical conditional detection delay than SCUSUM at comparable false-alarm levels.

This article introduces a sliding window model for defocus deblurring that achieves the best performance to date with extremely low memory usage. Named Swintormer, the method utilizes a diffusion model to generate latent prior features that assist in restoring more detailed images. It also extends the sliding window strategy to specialized Transformer blocks for efficient inference. Additionally, we have further optimized Multiply-Accumulate operations (Macs). Compared to the currently top-performing GRL method, our Swintormer model drastically reduces computational complexity from 140.35 GMACs to 8.02 GMacs, while also improving the Signal-to-Noise Ratio (SNR) for defocus deblurring from 27.04 dB to 27.07 dB. This new method allows for the processing of higher resolution images on devices with limited memory, significantly expanding potential application scenarios. The article concludes with an ablation study that provides an in-depth analysis of the impact of each network module on final performance. The source code and model will be available at the following website: https://github.com/bnm6900030/swintormer.