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core_ops.py
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core_ops.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import torch
import torch.fft as torch_fft
from torch.nn import functional as F
from datagen import crop
# Sense in Image space, exactly like in MoDL
# img -> mult (broad) -> FFT -> mask -> ksp
# ksp -> mask -> IFFT -> mult (conj) -> sum (coils) -> img
def TorchMoDLSense(mps_kernel, mask):
# Get image representation of padded maps kernel
img_y = mps_kernel
# Get masks with right sizes
mask_fw_ext = mask[None, ...]
mask_adj_ext = mask[None, ...]
# Forward
def forward_op(img_kernel):
# Pointwise complex multiply with maps
mult_result = img_kernel[None, ...] * img_y
# Convert back to k-space
result = torch_fft.ifftshift(mult_result, dim=(-2, -1))
result = torch_fft.fft2(result, dim=(-2, -1), norm='ortho')
result = torch_fft.fftshift(result, dim=(-2, -1))
# Multiply with mask
result = result * mask_fw_ext
return result
# Adjoint
def adjoint_op(ksp):
# Multiply input with mask and pad
ksp_padded = ksp * mask_adj_ext
# Get image representation of ksp
img_ksp = torch_fft.fftshift(ksp_padded, dim=(-2, -1))
img_ksp = torch_fft.ifft2(img_ksp, dim=(-2, -1), norm='ortho')
img_ksp = torch_fft.ifftshift(img_ksp, dim=(-2, -1))
# Pointwise complex multiply with complex conjugate maps
mult_result = img_ksp * torch.conj(img_y)
# Sum on coil axis
x_adj = torch.sum(mult_result, dim=0)
return x_adj
# Normal operator
def normal_op(img_kernel):
return adjoint_op(forward_op(img_kernel))
return forward_op, adjoint_op, normal_op
# Image in image space, exactly like in MoDL
# maps -> mult (broad) -> FFT -> mask -> ksp
# ksp -> mask -> IFFT -> mult (conj broad) -> maps
def TorchMoDLImage(img_kernel, mask):
# Get image representation of image kernel
img_x = img_kernel
# Get masks with right sizes
mask_fw_ext = mask[None, ...]
mask_adj_ext = mask[None, ...]
# Forward operator
def forward_op(mps_kernel):
# Pointwise complex multiply with maps
mult_result = mps_kernel * img_x
# Convert back to k-space
result = torch_fft.ifftshift(mult_result, dim=(-2, -1))
result = torch_fft.fft2(result, dim=(-2, -1), norm='ortho')
result = torch_fft.fftshift(result, dim=(-2, -1))
# Multiply with mask
result = result * mask_fw_ext
return result
# Adjoint operator
def adjoint_op(ksp):
# Multiply input with mask and pad
ksp_padded = ksp * mask_adj_ext
# Get image representations
img_ksp = torch_fft.fftshift(ksp_padded, dim=(-2, -1))
img_ksp = torch_fft.ifft2(img_ksp, dim=(-2, -1), norm='ortho')
img_ksp = torch_fft.ifftshift(img_ksp, dim=(-2, -1))
# Pointwise complex multiply (with conjugate image and broadcasting)
mult_result = img_ksp * torch.conj(img_x)[None, ...]
# Central crop
y_adj = mult_result
return y_adj
# Normal operator
def normal_op(mps_kernel):
return adjoint_op(forward_op(mps_kernel))
return forward_op, adjoint_op, normal_op
# Our 'hybrid' implementation
# ConvSense Forward - we're given an image kernel in image space, and we output k-space
# mask <- FFT <- pointwise mult with map kernel in image space <- image kernel in image space
# ConvSense Adjoint - we're given k-space, and we output an image kernel in image space
# mask -> IFFT -> pointwise mult with conj map kernel in image space -> estimated image kernel in image space
def TorchHybridSense(img_kernel_shape,
mps_kernel, mask,
img_full_shape,
ksp_padding, maps_padding):
# Get image representation of padded maps kernel
y_padded = F.pad(mps_kernel, (maps_padding[-2], maps_padding[-1],
maps_padding[-4], maps_padding[-3]))
# This only happens once
img_y = torch_fft.fftshift(y_padded, dim=(-2, -1))
img_y = torch_fft.ifft2(img_y, dim=(-2, -1), norm='ortho')
img_y = torch_fft.ifftshift(img_y, dim=(-2, -1))
# Get masks with right sizes
mask_fw_ext = mask[None, ...]
mask_adj_ext = mask[None, None, ...]
# Forward
def forward_op(img_kernel):
# Pointwise complex multiply with maps
mult_result = img_kernel[None, ...] * img_y
# Convert back to k-space
# !!! The squared normalization before cancels the required normalization here
result = torch_fft.ifftshift(mult_result, dim=(-2, -1))
result = torch_fft.fft2(result, dim=(-2, -1), norm='ortho')
result = torch_fft.fftshift(result, dim=(-2, -1))
# Central crop
result = crop(result, img_full_shape[-2], img_full_shape[-1])
# Multiply with mask
result = result * mask_fw_ext
return result
# Adjoint
def adjoint_op(ksp):
# Multiply input with mask and pad
ksp_padded = F.pad(ksp * mask_adj_ext[0], (
ksp_padding[-2], ksp_padding[-1],
ksp_padding[-4], ksp_padding[-3]))
# Get image representation of ksp
img_ksp = torch_fft.fftshift(ksp_padded, dim=(-2, -1))
img_ksp = torch_fft.ifft2(img_ksp, dim=(-2, -1), norm='ortho')
img_ksp = torch_fft.ifftshift(img_ksp, dim=(-2, -1))
# Pointwise complex multiply with complex conjugate maps
mult_result = img_ksp * torch.conj(img_y)
# Sum on coil axis
x_adj = torch.sum(mult_result, dim=0)
return x_adj
# Normal operator
def normal_op(img_kernel):
return adjoint_op(forward_op(img_kernel))
return forward_op, adjoint_op, normal_op
# ConvImage Forward - we input a map kernel in k-space, and we output k-space
# mask <- FFT <- pointwise mult with image kernel in image space <- IFFT <- pad with zeroes <- map kernel in k-space
# map kernel in k-space -> pad with zeroes -> IFFT ('ortho') -> pointwise mult with image kernel in image space -> FFT ('backward') -> crop -> mask -> coil images in k-space
# ConvImage Adjoint - we input k-space, and we output a map kernel in k-space
# coil images in k-space -> mask -> pad with zeroes -> IFFT ('ortho') -> pointwise mult with conj image kernel -> FFT ('backward') -> crop -> map kernel in k-space
def TorchHybridImage(mps_kernel_shape,
img_kernel, mask,
img_full_shape,
ksp_padding, maps_padding):
# Get image representation of image kernel
img_x = img_kernel
# Get masks with right sizes
mask_fw_ext = mask[None, ...]
mask_adj_ext = mask[None, None, ...]
# Forward operator
def forward_op(mps_kernel):
# Get image representation of padded maps kernel
y_padded = F.pad(mps_kernel, (maps_padding[-2], maps_padding[-1],
maps_padding[-4], maps_padding[-3]))
img_y = torch_fft.ifftshift(y_padded, dim=(-2, -1))
img_y = torch_fft.ifft2(img_y, dim=(-2, -1), norm='ortho')
img_y = torch_fft.fftshift(img_y, dim=(-2, -1))
# Pointwise complex multiply with image kernel
mult_result = img_y * img_kernel
# Convert back to k-space
# !!! The squared normalization cancels the required normalization here
result = torch_fft.fftshift(mult_result, dim=(-2, -1))
result = torch_fft.fft2(result, dim=(-2, -1), norm='backward')
result = torch_fft.ifftshift(result, dim=(-2, -1))
# Central crop
result = crop(result, img_full_shape[-2], img_full_shape[-1])
# Multiply with mask
result = result * mask_fw_ext
return result
# Adjoint operator
def adjoint_op(ksp):
# Multiply input with mask and pad
ksp_padded = F.pad(ksp * mask_adj_ext[0], (
ksp_padding[-2], ksp_padding[-1],
ksp_padding[-4], ksp_padding[-3]))
# Get image representations
img_ksp = torch_fft.ifftshift(ksp_padded, dim=(-2, -1))
img_ksp = torch_fft.ifft2(img_ksp, dim=(-2, -1), norm='ortho')
img_ksp = torch_fft.fftshift(img_ksp, dim=(-2, -1))
# Pointwise complex multiply (with conjugate image and broadcasting)
mult_result = img_ksp * torch.conj(img_x)[None, ...]
# Convert back to k-space
result = torch_fft.fftshift(mult_result, dim=(-2, -1))
result = torch_fft.fft2(result, dim=(-2, -1), norm='backward')
result = torch_fft.ifftshift(result, dim=(-2, -1))
# Central crop
y_adj = crop(result, mps_kernel_shape[-2], mps_kernel_shape[-1])
return y_adj
# Normal operator
def normal_op(mps_kernel):
return adjoint_op(forward_op(mps_kernel))
return forward_op, adjoint_op, normal_op