pytomography.projectors
#
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 \(\mathbb{V}\)
Subpackages#
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 corresponding projections \(g \in \mathbb{V}\) that would be produced by the imaging system. A system matrix consists of sequences of object-to-object and proj-to-proj 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 proj2proj_transforms can allow this system matrix to also model converging/diverging collimator configurations as well. |
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SPECT system matrix where the object space is a vector of length \(N\) consisting of the mean activities for each masks in |
- class pytomography.projectors.SystemMatrix(obj2obj_transforms, proj2proj_transforms, object_meta, proj_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 corresponding projections \(g \in \mathbb{V}\) that would be produced by the imaging system. A system matrix consists of sequences of object-to-object and proj-to-proj 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 proj mappings that occur after forward projection.
object_meta (ObjectMeta) – Object metadata.
proj_meta (ProjMeta) – Projection metadata.
proj2proj_transforms (list[pytomography.transforms.Transform]) –
- 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 proj where Ltheta is specified by self.proj_meta and angle_subset.
- Return type:
torch.tensor[batch_size, Ltheta, Lx, Lz]
- abstract backward(proj, angle_subset=None, return_norm_constant=False)#
Implements back projection \(H^T g\) on a set of projections \(g\).
- Parameters:
proj (torch.Tensor) – proj 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.projectors.SPECTSystemMatrix(obj2obj_transforms, proj2proj_transforms, object_meta, proj_meta, n_parallel=1)#
Bases:
pytomography.projectors.system_matrix.SystemMatrix
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.
- Parameters:
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.
- 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 projections where Ltheta is specified by self.proj_meta and angle_subset.
- Return type:
torch.tensor[batch_size, Ltheta, Lx, Lz]
- backward(proj, angle_subset=None, return_norm_constant=False)#
Applies back projection to
proj
for a SPECT imaging system.- Parameters:
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 \(j\) 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.projectors.SPECTSystemMatrixMaskedSegments(obj2obj_transforms, proj2proj_transforms, object_meta, proj_meta, masks)#
Bases:
SPECTSystemMatrix
SPECT system matrix where the object space is a vector of length \(N\) 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 \(f\) inside each of the masks.- Parameters:
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.
- forward(activities, angle_subset=None)#
Implements forward projection \(HUa\) on a vector of activities \(a\) corresponding to self.masks.
- Parameters:
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 \(j\) in formula above) when back projecting. Useful for ordered-subset reconstructions. Defaults to None, which assumes all angles are used.
- Returns:
Forward projected projections where Ltheta is specified by self.proj_meta and angle_subset.
- Return type:
torch.tensor[batch_size, Ltheta, Lx, Lz]
- backward(proj, angle_subset=None, prior=None, normalize=False, return_norm_constant=False)#
Implements back projection \(U^T H^T g\) on projections \(g\), returning a vector of activities for each mask region.
- Parameters:
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 \(j\) 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 \(\frac{1}{\sum_j H_{ij} + P_i}\) where \(P_i\) is given by the prior. Used, for example, during in MAP OSEM. Defaults to None.
normalize (bool) – Whether or not to divide result by \(\sum_j H_{ij}\)
return_norm_constant (bool) – Whether or not to return \(1/\sum_j H_{ij}\) along with back projection. Defaults to ‘False’.
- Returns:
the activities in each mask region.
- Return type:
torch.tensor[batch_size, n_masks]