from __future__ import annotations
import torch
import torch.nn as nn
import abc
import pytomography
from pytomography.transforms import Transform
from pytomography.metadata import ObjectMeta, ImageMeta
from pytomography.priors import Prior
from pytomography.utils import rotate_detector_z, pad_object, unpad_object, pad_image, unpad_image
[docs]class SystemMatrix():
r"""Update this
Args:
obj2obj_transforms (Sequence[Transform]): Sequence of object mappings that occur before forward projection.
im2im_transforms (Sequence[Transform]): Sequence of image mappings that occur after forward projection.
object_meta (ObjectMeta): Object metadata.
image_meta (ImageMeta): Image metadata.
"""
def __init__(
self,
obj2obj_transforms: list[Transform],
im2im_transforms: list[Transform],
object_meta: ObjectMeta,
image_meta: ImageMeta,
) -> None:
self.device = pytomography.device
self.obj2obj_transforms = obj2obj_transforms
self.im2im_transforms = im2im_transforms
self.object_meta = object_meta
self.image_meta = image_meta
self.initialize_correction_nets()
[docs] def initialize_correction_nets(self):
"""Initializes all mapping networks with the required object and image metadata corresponding to the projection network.
"""
for net in self.obj2obj_transforms:
net.configure(self.object_meta, self.image_meta)
for net in self.im2im_transforms:
net.configure(self.object_meta, self.image_meta)
[docs] def forward(
self,
object: torch.tensor,
angle_subset: list[int] = None,
) -> torch.tensor:
r"""Implements forward projection :math:`Hf` on an object :math:`f`.
Args:
object (torch.tensor[batch_size, Lx, Ly, Lz]): The object to be forward projected
angle_subset (list, optional): Only uses a subset of angles (i.e. only certain values of :math:`j` in formula above) when back projecting. Useful for ordered-subset reconstructions. Defaults to None, which assumes all angles are used.
Returns:
torch.tensor[batch_size, Ltheta, Lx, Lz]: Forward projected image where Ltheta is specified by `self.image_meta` and `angle_subset`.
"""
N_angles = self.image_meta.num_projections
object = object.to(self.device)
image = torch.zeros((object.shape[0],*self.image_meta.padded_shape)).to(self.device)
looper = range(N_angles) if angle_subset is None else angle_subset
for i in looper:
object_i = rotate_detector_z(pad_object(object), self.image_meta.angles[i])
for net in self.obj2obj_transforms:
object_i = net(object_i, i)
image[:,i] = object_i.sum(axis=1)
for net in self.im2im_transforms:
image = net(image)
return unpad_image(image)
[docs] def backward(
self,
image: torch.tensor,
angle_subset: list | None = None,
prior: Prior | None = None,
normalize: bool = False,
return_norm_constant: bool = False,
delta: float = 1e-11
) -> torch.tensor:
r"""Implements back projection :math:`H^T g` on an image :math:`g`.
Args:
image (torch.tensor[batch_size, Ltheta, Lr, Lz]): image which is to be back projected
angle_subset (list, optional): Only uses a subset of angles (i.e. only certain values of :math:`j` in formula above) when back projecting. Useful for ordered-subset reconstructions. Defaults to None, which assumes all angles are used.
prior (Prior, optional): If included, modifes normalizing factor to :math:`\frac{1}{\sum_j H_{ij} + P_i}` where :math:`P_i` is given by the prior. Used, for example, during in MAP OSEM. Defaults to None.
normalize (bool): Whether or not to divide result by :math:`\sum_j H_{ij}`
return_norm_constant (bool): Whether or not to return :math:`1/\sum_j H_{ij}` along with back projection. Defaults to 'False'.
delta (float, optional): Prevents division by zero when dividing by normalizing constant. Defaults to 1e-11.
Returns:
torch.tensor[batch_size, Lr, Lr, Lz]: the object obtained from back projection.
"""
# Box used to perform back projection
boundary_box_bp = pad_object(torch.ones((1, *self.object_meta.shape)).to(self.device), mode='back_project')
# Pad image and norm_image (norm_image used to compute sum_j H_ij)
norm_image = torch.ones(image.shape).to(self.device)
image = pad_image(image)
norm_image = pad_image(norm_image)
# First apply image mappings before back projecting
for net in self.im2im_transforms[::-1]:
image = net(image, mode='back_project')
norm_image = net(norm_image, mode='back_project')
# Setup for back projection
N_angles = self.image_meta.num_projections
object = torch.zeros([image.shape[0], *self.object_meta.padded_shape]).to(self.device)
norm_constant = torch.zeros([image.shape[0], *self.object_meta.padded_shape]).to(self.device)
looper = range(N_angles) if angle_subset is None else angle_subset
for i in looper:
# Perform back projection
object_i = image[:,i].unsqueeze(dim=1) * boundary_box_bp
norm_constant_i = norm_image[:,i].unsqueeze(dim=1) * boundary_box_bp
# Apply object mappings
for net in self.obj2obj_transforms[::-1]:
object_i, norm_constant_i = net(object_i, i, norm_constant=norm_constant_i)
# Add to total
norm_constant += rotate_detector_z(norm_constant_i, self.image_meta.angles[i], negative=True)
object += rotate_detector_z(object_i, self.image_meta.angles[i], negative=True)
# Unpad
norm_constant = unpad_object(norm_constant)
object = unpad_object(object)
# Apply prior
if prior:
norm_constant += prior()
if normalize:
object = (object+delta)/(norm_constant + delta)
# Return
if return_norm_constant:
return object, norm_constant+delta
else:
return object