pytomography.projectors.system_matrix#

Module Contents#

Classes#

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.

class pytomography.projectors.system_matrix.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()[source]#

Initializes all transforms used to build the system matrix

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]