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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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 |
- 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]) –
- abstract forward(object, **kwargs)[source]#
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)[source]#
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.ExtendedSystemMatrix(system_matrices, obj2obj_transforms=None, proj2proj_transforms=None)[source]#
Bases:
SystemMatrix
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.
system_matrices (Sequence[SystemMatrix]) –
proj2proj_transforms (Sequence[pytomography.transforms.Transform]) –
- forward(object, subset_idx=None)[source]#
Forward transform \(H' = \sum_n v_n \otimes B_n H_n A_n\), This adds an additional dimension to the projection space.
- Parameters:
object (torch.Tensor[1,Lx,Ly,Lz]) – Object to be forward projected. Must have a batch size of 1.
angle_subset (Sequence[int], 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.
subset_idx (int | None) –
- Returns:
Forward projection.
- Return type:
torch.Tensor[N_gates,…]
- backward(proj, subset_idx=None)[source]#
Back projection \(H' = \sum_n v_n^T \otimes A_n^T H_n^T B_n^T\). This maps an extended projection back to the original object space.
- Parameters:
proj (torch.Tensor[N,...]) – Projection data to be back-projected.
angle_subset (Sequence[int], 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.. Defaults to None.
subset_idx (int | None) –
- Returns:
Back projection.
- Return type:
torch.Tensor[1,Lx,Ly,Lz]