Source code for pytomography.projections.back_projection

from __future__ import annotations
import torch
from pytomography.utils.helper_functions import rotate_detector_z, pad_object, unpad_object, pad_image
from .projection import ProjectionNet
from pytomography.priors import Prior

[docs]class BackProjectionNet(ProjectionNet): r"""Implements a back projection of mathematical form :math:`f_i = \frac{1}{\sum_j c_{ij}}\sum_{j} c_{ij} g_j`. where :math:`f_j` is an object, :math:`g_j` is an image, and :math:`c_{ij}` is the system matrix given by the various phenonemon modeled (e.g. atteunation correction/PSF). Subclass of the ``ProjectionNet`` class."""
[docs] def forward( 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 on an image, returning an object. 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 c_{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 c_{ij}` return_norm_constant (bool): Whether or not to return :math:`1/\sum_j c_{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 c_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_nets[::-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_nets[::-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