Scripts/utils_spud.py

import torch
import torch_dct as dct

import torch.nn.functional as F


def modulo(x, L):
    positive = x > 0
    x = x % L
    x = torch.where( ( x == 0) &  positive, L, x)
    return x


def center_modulo(x, L):
    return modulo(x + L/2, L) - L/2


def hard_threshold(x, threshold):
    return torch.where(torch.abs(x) > threshold, x, torch.zeros_like(x))


def recons_spud(y, threshold=0.1,  mx=1.0):
        
    # Mdx_y = M( Delta_x @ y ) , Mdy_y = M( Delta_y @ y )
    Mdx_y = F.pad( center_modulo(torch.diff(y, 1, dim=-1), mx), (1, 0), mode='constant')
    Mdy_y = F.pad( center_modulo(torch.diff(y, 1, dim=-2), mx), (0, 0, 1, 0), mode='constant')

    # DTMDy = D^T ( Mdx_y, Mdy_y )
    rho =  - ( torch.diff(F.pad(Mdx_y, (0, 1)), 1, dim=-1) + torch.diff(F.pad(Mdy_y, (0,0, 0, 1)), 1, dim=-2) )

    dct_rho = dct.dct_2d(rho, norm='ortho')

    NX, MX = rho.shape[-1], rho.shape[-2]
    I, J = torch.meshgrid(torch.arange(0, MX), torch.arange(0, NX), indexing="ij")
    I, J = I.to(rho.device), J.to(rho.device)

    I, J = I.unsqueeze(0).unsqueeze(0), J.unsqueeze(0).unsqueeze(0)

    denom = 2 * (  2 - ( torch.cos(torch.pi * I / MX ) + torch.cos(torch.pi * J / NX ) ) )
    denom = denom.to(rho.device)

    dct_phi = dct_rho / denom
    dct_phi[..., 0, 0] = 0

    dct_phi = hard_threshold(dct_phi, threshold)

    phi = dct.idct_2d(dct_phi, norm='ortho')
    phi = phi - phi.min()
    phi = phi / phi.max()

    return phi