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"""
Guassian Process Regression.
Inspired by: https://onlinelibrary.wiley.com/doi/pdf/10.1002/smll.202002878?casa_token=OP1n_oLqe4kAAAAA%3Aiovq39gdeNfEIR8Vyi_FRd3Ec9lz8cDm3m9MtmCoOXbg6w1ohs5YPom5x9uVK9S3wsqmssIPFzfsCIBM9w
"""
from concurrent.futures import ThreadPoolExecutor
import gpim
import gpytorch
import torch
import torch.nn as nn
import torch.nn.functional as F
import numpy as np
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF, WhiteKernel
class GPR:
def __init__(self, sr: int = 2):
self.sr = sr
self.gpr_model = None
def __call__(self, x: torch.Tensor) -> torch.Tensor:
if self.gpr_model is None:
self.gpr_model = self.gpr_sr(x[0, ...])
x_np = x.clone().cpu().numpy()
if x_np.ndim == 2:
x_np = x_np[None, ...]
def process_image(img):
H, W = img.shape
H_hr, W_hr = self.sr * H, self.sr * W
grid_x = np.linspace(0, 1, H_hr)
grid_y = np.linspace(0, 1, W_hr)
xx, yy = np.meshgrid(grid_x, grid_y, indexing='ij')
X_pred = np.column_stack([xx.ravel(), yy.ravel()])
y_pred, y_std = self.gpr_model.predict(X_pred, return_std=True)
y_pred_img = y_pred.reshape(H_hr, W_hr)
return torch.Tensor(y_pred_img)
with ThreadPoolExecutor() as executor:
batch_outputs = list(executor.map(process_image, x_np))
return torch.stack(batch_outputs, dim=0)
def gpr_sr(self, y_sparse: torch.Tensor):
"""
Perform super-resolution on an input tensor `y_sparse` with shape (H, W)
"""
x = y_sparse.clone()
x = x.cpu().numpy()
H, W = x.shape
# create a train/test set
train_indices = np.argwhere(~np.isnan(x))
y_train = x[~np.isnan(x)]
X_train = train_indices.astype(np.float64)
X_train[:, 0] /= (H - 1)
X_train[:, 1] /= (W - 1)
# normalize -> [0, 1]
X_train = train_indices.astype(np.float64)
X_train[:, 0] /= (H - 1)
X_train[:, 1] /= (W - 1)
kernel = RBF(length_scale=0.1, length_scale_bounds=(1e-2, 1e2)) + WhiteKernel(noise_level=1e-3, noise_level_bounds=(1e-5, 1e1))
gp = GaussianProcessRegressor(kernel=kernel, normalize_y=True)
gp.fit(X_train, y_train)
return gp
class GPReconstuctionInpainter(nn.Module):
"""
[DEP]: An older implementation.
"""
def __init__(
self,
):
"""
...
"""
super(GPReconstuctionInpainter, self).__init__()
@torch.enable_grad()
def forward(self, y_sparse: torch.Tensor) -> torch.Tensor:
"""
:param y_sparse: EXACTLY [1, 3, 128, 128]
Following the examples provided in gpim repo:
https://github.com/ziatdinovmax/GPim/blob/master/examples/notebooks/GP_2D3D_images.ipynb.
"""
# HACK: assume y_sparse has EXACTLY shape: [1, 3, 128, 128]
R = y_sparse.clone().cpu()[0, 0, :, :]
R = R.numpy().astype(float)
# HACK: we hard coded the sparsity of incoming y_sparse, assume always 50%
R[:, ::2] = np.NaN
# Get full (ideal) grid indices
X_full = gpim.utils.get_full_grid(R, dense_x=1)
# Get sparse grid indices
X_sparse = gpim.utils.get_sparse_grid(R)
# run GP reconstruction to obtain mean prediction and uncertainty for each predictied point
recon = gpim.reconstructor(
X_sparse,
R,
X_full,
learning_rate=0.1,
iterations=2,
use_gpu=True,
verbose=False,
)
# train + predict
mean, sd, hyperparams = recon.run()
e1, e2 = R.shape
# (128, 128)
pred = mean.reshape(e1, e2)
# (128, 128) -> (3, 128, 128)
pred = np.stack([pred] * 3, axis=0)
# (3, 128, 128) -> (1, 3, 128, 128)
pred = np.expand_dims(pred, 0)
# -> tensor -> gpu
pred = torch.Tensor(pred).cuda()
return pred
@staticmethod
def get(weights=None):
return GPReconstuctionInpainter()
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