Source code for pytomography.transforms.SPECT.psf
from __future__ import annotations
from typing import Sequence
import torch
import torch.nn as nn
import numpy as np
import pytomography
from pytomography.utils import get_distance, compute_pad_size, pad_object, pad_object_z, unpad_object_z, rotate_detector_z, unpad_object
from pytomography.transforms import Transform
from pytomography.metadata import ObjectMeta, ImageMeta, PSFMeta
import time
[docs]class GaussianBlurNet(nn.Module):
def __init__(self, layer_r, layer_z=None):
super(GaussianBlurNet, self).__init__()
self.layer_r = layer_r
self.layer_z = layer_z
[docs] def forward(self, input):
output = self.layer_r(torch.permute(input[0],(1,0,2)))
# If 2D blurring
if self.layer_z:
output = self.layer_z(torch.permute(output,(2,1,0)))
return torch.permute(output,(1,2,0)).unsqueeze(0)
[docs]def get_1D_PSF_layer(
sigmas: np.array,
kernel_size: int,
) -> torch.nn.Conv1d:
"""Creates a 1D convolutional layer that is used for PSF modeling.
Args:
sigmas (array): Array of length Lx corresponding to blurring (sigma of Gaussian) as a function of distance from scanner
kernel_size (int): Size of the kernel used in each layer. Needs to be large enough to cover most of Gaussian
Returns:
torch.nn.Conv2d: Convolutional neural network layer used to apply blurring to objects of shape [batch_size, Lx, Ly, Lz]
"""
N = len(sigmas)
layer = nn.Conv1d(N, N, kernel_size, groups=N, padding='same',
padding_mode='zeros', bias=0, device=pytomography.device)
x = torch.arange(-int(kernel_size//2), int(kernel_size//2)+1).to(pytomography.device).unsqueeze(0).unsqueeze(0).repeat((N,1,1))
sigmas = torch.tensor(sigmas).to(pytomography.device).to(pytomography.dtype).reshape((N,1,1))
kernel = torch.exp(-x**2 / (2*sigmas**2 + pytomography.delta))
kernel = kernel / kernel.sum(axis=-1).unsqueeze(-1)
layer.weight.data = kernel.to(pytomography.dtype)
return layer
[docs]class SPECTPSFTransform(Transform):
"""obj2obj transform used to model the effects of PSF blurring in SPECT. The smoothing kernel used to apply PSF modeling uses a Gaussian kernel with width :math:`\sigma` dependent on the distance of the point to the detector; that information is specified in the ``PSFMeta`` parameter.
Args:
psf_meta (PSFMeta): Metadata corresponding to the parameters of PSF blurring
"""
def __init__(
self,
psf_meta: PSFMeta,
) -> None:
"""Initializer that sets corresponding psf parameters"""
super(SPECTPSFTransform, self).__init__()
self.psf_meta = psf_meta
[docs] def configure(
self,
object_meta: ObjectMeta,
image_meta: ImageMeta
) -> None:
"""Function used to initalize the transform using corresponding object and image metadata
Args:
object_meta (ObjectMeta): Object metadata.
image_meta (ImageMeta): Image metadata.
"""
super(SPECTPSFTransform, self).configure(object_meta, image_meta)
self.layers = {}
for radius in np.unique(image_meta.radii):
kernel_size_r = self.compute_kernel_size(radius, axis=0)
kernel_size_z = self.compute_kernel_size(radius, axis=2)
# Compute sigmas and normalize to pixel units
sigma_r = self.get_sigma(radius)/object_meta.dx
sigma_z = self.get_sigma(radius)/object_meta.dz
layer_r = get_1D_PSF_layer(sigma_r, kernel_size_r)
layer_z = get_1D_PSF_layer(sigma_z, kernel_size_z)
if self.psf_meta.kernel_dimensions=='2D':
self.layers[radius] = GaussianBlurNet(layer_r, layer_z)
else: # 1D blurring
self.layers[radius] = GaussianBlurNet(layer_r)
[docs] def compute_kernel_size(self, radius, axis) -> int:
"""Function used to compute the kernel size used for PSF blurring. In particular, uses the ``min_sigmas`` attribute of ``PSFMeta`` to determine what the kernel size should be such that the kernel encompasses at least ``min_sigmas`` at all points in the object.
Returns:
int: The corresponding kernel size used for PSF blurring.
"""
sigma_max = max(self.get_sigma(radius))
sigma_max /= self.object_meta.dr[axis]
return (np.ceil(sigma_max * self.psf_meta.min_sigmas)*2 + 1).astype(int)
[docs] def get_sigma(
self,
radius: float,
) -> np.array:
"""Uses PSF Meta data information to get blurring :math:`\sigma` as a function of distance from detector.
Args:
radius (float): The distance from the detector.
Returns:
array: An array of length Lx corresponding to blurring at each point along the 1st axis in object space
"""
dim = self.object_meta.shape[0] + 2*compute_pad_size(self.object_meta.shape[0])
distances = get_distance(dim, radius, self.object_meta.dx)
sigma = self.psf_meta.sigma_fit(distances, *self.psf_meta.sigma_fit_params)
return sigma
[docs] def apply_psf(self, object, ang_idx):
object_return = []
for i in range(len(ang_idx)):
object_temp = object[i].unsqueeze(0)
object_temp = self.layers[self.image_meta.radii[ang_idx[i]]](object_temp)
object_return.append(object_temp)
return torch.vstack(object_return)
@torch.no_grad()
[docs] def forward(
self,
object_i: torch.Tensor,
ang_idx: int,
) -> torch.tensor:
r"""Applies the PSF transform :math:`A:\mathbb{U} \to \mathbb{U}` for the situation where an object is being detector by a detector at the :math:`+x` axis.
Args:
object_i (torch.tensor): Tensor of size [batch_size, Lx, Ly, Lz] being projected along its first axis
ang_idx (int): The projection indices: used to find the corresponding angle in image space corresponding to each projection angle in ``object_i``.
Returns:
torch.tensor: Tensor of size [batch_size, Lx, Ly, Lz] such that projection of this tensor along the first axis corresponds to n PSF corrected projection.
"""
return self.apply_psf(object_i, ang_idx)
@torch.no_grad()
[docs] def backward(
self,
object_i: torch.Tensor,
ang_idx: int,
norm_constant: torch.Tensor | None = None,
) -> torch.tensor:
r"""Applies the transpose of the PSF transform :math:`A^T:\mathbb{U} \to \mathbb{U}` for the situation where an object is being detector by a detector at the :math:`+x` axis. Since the PSF transform is a symmetric matrix, its implemtation is the same as the ``forward`` method.
Args:
object_i (torch.tensor): Tensor of size [batch_size, Lx, Ly, Lz] being projected along its first axis
ang_idx (int): The projection indices: used to find the corresponding angle in image space corresponding to each projection angle in ``object_i``.
norm_constant (torch.tensor, optional): A tensor used to normalize the output during back projection. Defaults to None.
Returns:
torch.tensor: Tensor of size [batch_size, Lx, Ly, Lz] such that projection of this tensor along the first axis corresponds to n PSF corrected projection.
"""
if norm_constant is not None:
object_i = self.apply_psf(object_i, ang_idx)
norm_constant = self.apply_psf(norm_constant, ang_idx)
return object_i, norm_constant
else:
return self.apply_psf(object_i, ang_idx)