from __future__ import annotations
import torch
import pytomography
from pytomography.transforms import Transform
from pytomography.metadata import SPECTObjectMeta, SPECTImageMeta
from pytomography.priors import Prior
from pytomography.utils import rotate_detector_z, pad_object, unpad_object, pad_image, unpad_image
from ..system_matrix import SystemMatrix
[docs]class SPECTSystemMatrix(SystemMatrix):
r"""System matrix for SPECT imaging. By default, this applies to parallel hole collimators, but appropriate use of `im2im_transforms` can allow this system matrix to also model converging/diverging collimator configurations as well.
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 (SPECTObjectMeta): SPECT Object metadata.
image_meta (SPECTImageMeta): SPECT Image metadata.
n_parallel (int): Number of projections to use in parallel when applying transforms. More parallel events may speed up reconstruction time, but also increases GPU usage. Defaults to 1.
"""
def __init__(
self,
obj2obj_transforms: list[Transform],
im2im_transforms: list[Transform],
object_meta: SPECTObjectMeta,
image_meta: SPECTImageMeta,
n_parallel = 1,
) -> None:
super(SPECTSystemMatrix, self).__init__(obj2obj_transforms, im2im_transforms, object_meta, image_meta)
self.n_parallel = n_parallel
[docs] def forward(
self,
object: torch.tensor,
angle_subset: list[int] = None,
) -> torch.tensor:
r"""Applies forward projection to ``object`` for a SPECT imaging system.
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(pytomography.device)
image = torch.zeros((object.shape[0],*self.image_meta.padded_shape)).to(pytomography.device)
angle_indices = torch.arange(N_angles) if angle_subset is None else angle_subset
# Loop through all angles (or groups of angles in parallel)
for i in range(0, len(angle_indices), self.n_parallel):
# Get angle indices
angle_indices_single_batch_i = angle_indices[i:i+self.n_parallel]
angle_indices_i = angle_indices_single_batch_i.repeat(object.shape[0])
# Format Object
object_i = torch.repeat_interleave(object, len(angle_indices_single_batch_i), 0)
object_i = pad_object(object_i)
object_i = rotate_detector_z(object_i, self.image_meta.angles[angle_indices_i])
# Apply object 2 object transforms
for transform in self.obj2obj_transforms:
object_i = transform.forward(object_i, angle_indices_i)
# Reshape to 5D tensor of shape [batch_size, N_parallel, Lx, Ly, Lz]
object_i = object_i.reshape((object.shape[0], -1, *self.object_meta.padded_shape))
image[:,angle_indices_single_batch_i] = object_i.sum(axis=2)
for transform in self.im2im_transforms:
image = transform.forward(image)
return unpad_image(image)
[docs] def backward(
self,
image: torch.tensor,
angle_subset: list | None = None,
return_norm_constant: bool = False,
) -> torch.tensor:
r"""Applies back projection to ``image`` for a SPECT imaging system.
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.
return_norm_constant (bool): Whether or not to return :math:`1/\sum_j H_{ij}` along with back projection. Defaults to 'False'.
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(pytomography.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(pytomography.device)
image = pad_image(image)
norm_image = pad_image(norm_image)
# First apply image transforms before back projecting
for transform in self.im2im_transforms[::-1]:
image, norm_image = transform.backward(image, norm_image)
# Setup for back projection
N_angles = self.image_meta.num_projections
object = torch.zeros([image.shape[0], *self.object_meta.padded_shape]).to(pytomography.device)
norm_constant = torch.zeros([image.shape[0], *self.object_meta.padded_shape]).to(pytomography.device)
angle_indices = torch.arange(N_angles) if angle_subset is None else angle_subset
for i in range(0, len(angle_indices), self.n_parallel):
angle_indices_single_batch_i = angle_indices[i:i+self.n_parallel]
angle_indices_i = angle_indices_single_batch_i.repeat(object.shape[0])
# Perform back projection
object_i = image[:,angle_indices_single_batch_i].flatten(0,1).unsqueeze(1) * boundary_box_bp
norm_constant_i = norm_image[:,angle_indices_single_batch_i].flatten(0,1).unsqueeze(1) * boundary_box_bp
# Apply object mappings
for transform in self.obj2obj_transforms[::-1]:
object_i, norm_constant_i = transform.backward(object_i, angle_indices_i, norm_constant=norm_constant_i)
# Rotate all objects by by their respective angle
object_i = rotate_detector_z(object_i, self.image_meta.angles[angle_indices_i], negative=True)
norm_constant_i = rotate_detector_z(norm_constant_i, self.image_meta.angles[angle_indices_i], negative=True)
# Reshape to 5D tensor of shape [batch_size, N_parallel, Lx, Ly, Lz]
object_i = object_i.reshape((object.shape[0], -1, *self.object_meta.padded_shape))
norm_constant_i = norm_constant_i.reshape((object.shape[0], -1, *self.object_meta.padded_shape))
# Add to total by summing over the N_parallel dimension (sum over all angles)
object += object_i.sum(axis=1)
norm_constant += norm_constant_i.sum(axis=1)
# Unpad
norm_constant = unpad_object(norm_constant)
object = unpad_object(object)
# Return
if return_norm_constant:
return object, norm_constant+pytomography.delta
else:
return object
[docs]class SPECTSystemMatrixMaskedSegments(SPECTSystemMatrix):
r"""SPECT system matrix where the object space is a vector of length :math:`N` consisting of the mean activities for each masks in ``masks``. This system matrix can be used in reconstruction algorithms to obtain maximum liklihood estimations for the average value of :math:`f` inside each of the masks.
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 (SPECTObjectMeta): SPECT Object metadata.
image_meta (SPECTImageMeta): SPECT Image metadata.
masks (torch.Tensor): Masks corresponding to each segmented region.
"""
def __init__(
self,
obj2obj_transforms: list[Transform],
im2im_transforms: list[Transform],
object_meta: SPECTObjectMeta,
image_meta: SPECTImageMeta,
masks: torch.Tensor
) -> None:
super(SPECTSystemMatrixMaskedSegments, self).__init__(obj2obj_transforms, im2im_transforms, object_meta, image_meta)
self.masks = masks.to(pytomography.device)
[docs] def forward(
self,
activities: torch.Tensor,
angle_subset: list[int] = None,
) -> torch.Tensor:
r"""Implements forward projection :math:`HUa` on a vector of activities :math:`a` corresponding to `self.masks`.
Args:
activities (torch.tensor[batch_size, n_masks]): Activities in each mask region.
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`.
"""
object = 0
activities = activities.reshape((*activities.shape, 1, 1, 1)).to(pytomography.device)
object = (activities*self.masks).sum(axis=1)
return super(SPECTSystemMatrixMaskedSegments, self).forward(object, angle_subset)
[docs] def backward(
self,
image: torch.Tensor,
angle_subset: list | None = None,
prior: Prior | None = None,
normalize: bool = False,
return_norm_constant: bool = False,
) -> torch.Tensor:
"""Implements back projection :math:`U^T H^T g` on an image :math:`g`, returning a vector of activities for each mask region.
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'.
Returns:
torch.tensor[batch_size, n_masks]: the activities in each mask region.
"""
object, norm_constant = super(SPECTSystemMatrixMaskedSegments, self).backward(image, angle_subset, prior, normalize=False, return_norm_constant = True, delta = pytomography.delta)
activities = (object.unsqueeze(dim=1) * self.masks).sum(axis=(-1,-2,-3))
norm_constant = (norm_constant.unsqueeze(dim=1) * self.masks).sum(axis=(-1,-2,-3))
if normalize:
activities = (activities+pytomography.delta)/(norm_constant + pytomography.delta)
if return_norm_constant:
return activities, norm_constant+pytomography.delta
else:
return activities