pytomography.projections.SPECT.spect_system_matrix
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Module Contents#
Classes#
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. |
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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.projections.SPECT.spect_system_matrix.SPECTSystemMatrix(obj2obj_transforms, im2im_transforms, object_meta, image_meta, n_parallel=1)[source]#
Bases:
pytomography.projections.system_matrix.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 (SPECTObjectMeta) – SPECT Object metadata.
image_meta (SPECTImageMeta) – SPECT 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)[source]#
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)[source]#
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]
- class pytomography.projections.SPECT.spect_system_matrix.SPECTSystemMatrixMaskedSegments(obj2obj_transforms, im2im_transforms, object_meta, image_meta, masks)[source]#
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.
im2im_transforms (Sequence[Transform]) – Sequence of image mappings that occur after forward projection.
object_meta (SPECTObjectMeta) – SPECT Object metadata.
image_meta (SPECTImageMeta) – SPECT Image metadata.
masks (torch.Tensor) – Masks corresponding to each segmented region.
- forward(activities, angle_subset=None)[source]#
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 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, prior=None, normalize=False, return_norm_constant=False)[source]#
Implements back projection \(U^T H^T g\) on an image \(g\), returning a vector of activities for each mask region.
- 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 \(j\) 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:`
- rac{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:
torch.tensor[batch_size, n_masks]: the activities in each mask region.
- Parameters:
image (torch.Tensor) –
angle_subset (list | None) –
prior (Prior | None) –
normalize (bool) –
return_norm_constant (bool) –
- Return type:
torch.Tensor