pytomography.projections
#
This module contains classes/functionality for operators that map between distinct vector spaces. One (very important) operator of this form is the system matrix \(H:\mathbb{U} \to \mathbb{V}\), which maps from object space \(\mathbb{U}\) to image space \(\mathbb{V}\)
Submodules#
Package Contents#
Classes#
Abstract class for a general system matrix \(H:\mathbb{U} \to \mathbb{V}\) which takes in an object \(f \in \mathbb{U}\) and maps it to a corresponding image \(g \in \mathbb{V}\) that would be produced by the imaging system. A system matrix consists of sequences of object-to-object and image-to-image transforms that model various characteristics of the imaging system, such as attenuation and blurring. While the class implements the operator \(H:\mathbb{U} \to \mathbb{V}\) through the |
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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. |
- class pytomography.projections.SystemMatrix(obj2obj_transforms, im2im_transforms, object_meta, image_meta)[source]#
Abstract class for a general system matrix \(H:\mathbb{U} \to \mathbb{V}\) which takes in an object \(f \in \mathbb{U}\) and maps it to a corresponding image \(g \in \mathbb{V}\) that would be produced by the imaging system. A system matrix consists of sequences of object-to-object and image-to-image transforms that model various characteristics of the imaging system, such as attenuation and blurring. While the class implements the operator \(H:\mathbb{U} \to \mathbb{V}\) through the
forward
method, it also implements \(H^T:\mathbb{V} \to \mathbb{U}\) through the backward method, required during iterative reconstruction algorithms such as OSEM.- Parameters:
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.
- initialize_transforms()#
Initializes all transforms used to build the system matrix
- abstract forward(object, **kwargs)#
Implements forward projection \(Hf\) on an object \(f\).
- Parameters:
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 \(j\) in formula above) when back projecting. Useful for ordered-subset reconstructions. Defaults to None, which assumes all angles are used.
- Returns:
Forward projected image where Ltheta is specified by self.image_meta and angle_subset.
- Return type:
torch.tensor[batch_size, Ltheta, Lx, Lz]
- abstract backward(image, angle_subset=None, return_norm_constant=False)#
Implements back projection \(H^T g\) on an image \(g\).
- Parameters:
image (torch.Tensor) – image which is to be back projected
angle_subset (list, optional) – Only uses a subset of angles (i.e. only certain values of \(j\) 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 \(1/\sum_j H_{ij}\) along with back projection. Defaults to ‘False’.
- Returns:
the object obtained from back projection.
- Return type:
torch.tensor[batch_size, Lr, Lr, Lz]
- class pytomography.projections.SPECTSystemMatrix(obj2obj_transforms, im2im_transforms, object_meta, image_meta, n_parallel=1)[source]#
Bases:
SystemMatrix
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.
- Parameters:
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.
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.
- forward(object, angle_subset=None)#
Applies forward projection to
object
for a SPECT imaging system.- Parameters:
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 \(j\) in formula above) when back projecting. Useful for ordered-subset reconstructions. Defaults to None, which assumes all angles are used.
- Returns:
Forward projected image where Ltheta is specified by self.image_meta and angle_subset.
- Return type:
torch.tensor[batch_size, Ltheta, Lx, Lz]
- backward(image, angle_subset=None, return_norm_constant=False)#
Applies back projection to
image
for a SPECT imaging system.- Parameters:
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 \(j\) 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 \(1/\sum_j H_{ij}\) along with back projection. Defaults to ‘False’.
- Returns:
the object obtained from back projection.
- Return type:
torch.tensor[batch_size, Lr, Lr, Lz]