Source code for pytomography.projectors.SPECT.spect_system_matrix

from __future__ import annotations
import torch
import pytomography
from pytomography.transforms import Transform, RotationTransform
from pytomography.metadata import SPECTObjectMeta, SPECTProjMeta
from pytomography.priors import Prior
from pytomography.utils import pad_object, unpad_object, pad_proj, unpad_proj
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 `proj2proj_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. proj2proj_transforms (Sequence[Transform]): Sequence of proj mappings that occur after forward projection. object_meta (SPECTObjectMeta): SPECT Object metadata. proj_meta (SPECTProjMeta): SPECT projection 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], proj2proj_transforms: list[Transform], object_meta: SPECTObjectMeta, proj_meta: SPECTProjMeta, n_parallel = 1, ) -> None: super(SPECTSystemMatrix, self).__init__(obj2obj_transforms, proj2proj_transforms, object_meta, proj_meta) self.n_parallel = n_parallel self.rotation_transform = RotationTransform()
[docs] def compute_normalization_factor(self, subset_idx : int | None = None) -> torch.tensor: """Function used to get normalization factor :math:`H^T_m 1` corresponding to projection subset :math:`m`. Args: subset_idx (int | None, optional): Index of subset. If none, then considers all projections. Defaults to None. Returns: torch.Tensor: normalization factor :math:`H^T_m 1` """ norm_proj = torch.ones((1, *self.proj_meta.shape)).to(pytomography.device) if subset_idx is not None: norm_proj = norm_proj[:,self.subset_indices_array[subset_idx]] return self.backward(norm_proj, subset_idx)
[docs] def set_n_subsets( self, n_subsets: int ) -> list: """Sets the subsets for this system matrix given ``n_subsets`` total subsets. Args: n_subsets (int): number of subsets used in OSEM """ indices = torch.arange(self.proj_meta.shape[0]).to(torch.long).to(pytomography.device) subset_indices_array = [] for i in range(n_subsets): subset_indices_array.append(indices[i::n_subsets]) self.subset_indices_array = subset_indices_array
[docs] def get_projection_subset( self, projections: torch.tensor, subset_idx: int ) -> torch.tensor: """Gets the subset of projections :math:`g_m` corresponding to index :math:`m`. Args: projections (torch.tensor): full projections :math:`g` subset_idx (int): subset index :math:`m` Returns: torch.tensor: subsampled projections :math:`g_m` """ return projections[:,self.subset_indices_array[subset_idx]]
[docs] def get_weighting_subset( self, subset_idx: int ) -> float: r"""Computes the relative weighting of a given subset (given that the projection space is reduced). This is used for scaling parameters relative to :math:`H_m^T 1` in reconstruction algorithms, such as prior weighting :math:`\beta` Args: subset_idx (int): Subset index Returns: float: Weighting for the subset. """ return len(self.subset_indices_array[subset_idx]) / self.proj_meta.num_projections
[docs] def forward( self, object: torch.tensor, subset_idx: int | None = 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 subset_idx (int, optional): Only uses a subset of angles :math:`g_m` corresponding to the provided subset index :math:`m`. If None, then defaults to the full projections :math:`g`. Returns: torch.tensor: forward projection estimate :math:`g_m=H_mf` """ # Deal with subset stuff if subset_idx is not None: angle_subset = self.subset_indices_array[subset_idx] N_angles = self.proj_meta.num_projections if subset_idx is None else len(angle_subset) angle_indices = torch.arange(N_angles) if subset_idx is None else angle_subset # Start projection object = object.to(pytomography.device) proj = torch.zeros( (object.shape[0],N_angles,*self.proj_meta.padded_shape[1:]) ).to(pytomography.device) # 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) # beta = 270 - phi, and backward transform called because projection should be at +beta (requires inverse rotation of object) object_i = self.rotation_transform.backward(object_i, 270-self.proj_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)) proj[:,i:i+self.n_parallel] = object_i.sum(axis=2) for transform in self.proj2proj_transforms: proj = transform.forward(proj) return unpad_proj(proj)
[docs] def backward( self, proj: torch.tensor, subset_idx: int | None = None, return_norm_constant: bool = False, ) -> torch.tensor: r"""Applies back projection to ``proj`` for a SPECT imaging system. Args: proj (torch.tensor): projections :math:`g` which are to be back projected subset_idx (int, optional): Only uses a subset of angles :math:`g_m` corresponding to the provided subset index :math:`m`. If None, then defaults to the full projections :math:`g`. return_norm_constant (bool): Whether or not to return :math:`H_m^T 1` along with back projection. Defaults to 'False'. Returns: torch.tensor: the object :math:`\hat{f} = H_m^T g_m` obtained via back projection. """ # Deal with subset stuff if subset_idx is not None: angle_subset = self.subset_indices_array[subset_idx] N_angles = self.proj_meta.num_projections if subset_idx is None else len(angle_subset) angle_indices = torch.arange(N_angles) if subset_idx is None else angle_subset # 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 proj and norm_proj (norm_proj used to compute sum_j H_ij) norm_proj = torch.ones(proj.shape).to(pytomography.device) proj = pad_proj(proj) norm_proj = pad_proj(norm_proj) # First apply proj transforms before back projecting for transform in self.proj2proj_transforms[::-1]: if return_norm_constant: proj, norm_proj = transform.backward(proj, norm_proj) else: proj = transform.backward(proj) # Setup for back projection object = torch.zeros([proj.shape[0], *self.object_meta.padded_shape]).to(pytomography.device) norm_constant = torch.zeros([proj.shape[0], *self.object_meta.padded_shape]).to(pytomography.device) for i in range(0, len(angle_indices), self.n_parallel): angle_indices_i = angle_indices[i:i+self.n_parallel] # Perform back projection object_i = proj[:,i:i+self.n_parallel].flatten(0,1).unsqueeze(1) * boundary_box_bp norm_constant_i = norm_proj[:,i:i+self.n_parallel].flatten(0,1).unsqueeze(1) * boundary_box_bp # Apply object mappings for transform in self.obj2obj_transforms[::-1]: if return_norm_constant: object_i, norm_constant_i = transform.backward(object_i, angle_indices_i, norm_constant=norm_constant_i) else: object_i = transform.backward(object_i, angle_indices_i) # Rotate all objects by by their respective angle object_i = self.rotation_transform.forward(object_i, 270-self.proj_meta.angles[angle_indices_i]) norm_constant_i = self.rotation_transform.forward(norm_constant_i, 270-self.proj_meta.angles[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)) 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 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. proj2proj_transforms (Sequence[Transform]): Sequence of proj mappings that occur after forward projection. object_meta (SPECTObjectMeta): SPECT Object metadata. proj_meta (SPECTProjMeta): SPECT proj metadata. masks (torch.Tensor): Masks corresponding to each segmented region. """ def __init__( self, obj2obj_transforms: list[Transform], proj2proj_transforms: list[Transform], object_meta: SPECTObjectMeta, proj_meta: SPECTProjMeta, masks: torch.Tensor ) -> None: super(SPECTSystemMatrixMaskedSegments, self).__init__(obj2obj_transforms, proj2proj_transforms, object_meta, proj_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 projections where Ltheta is specified by `self.proj_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, proj: torch.Tensor, angle_subset: list | None = None, prior: Prior | None = None, normalize: bool = False, return_norm_constant: bool = False, ) -> torch.Tensor: r"""Implements back projection :math:`U^T H^T g` on projections :math:`g`, returning a vector of activities for each mask region. Args: proj (torch.tensor[batch_size, Ltheta, Lr, Lz]): projections which are 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(proj, 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