pytomography.transforms.SPECT#

Submodules#

Package Contents#

Classes#

SPECTAttenuationTransform

obj2obj transform used to model the effects of attenuation in SPECT.

SPECTPSFTransform

obj2obj transform used to model the effects of PSF blurring in SPECT. The smoothing kernel used to apply PSF modeling uses a Gaussian kernel with width \(\sigma\) dependent on the distance of the point to the detector; that information is specified in the PSFMeta parameter.

CutOffTransform

im2im transformation used to set pixel values equal to zero at the first and last few z slices. This is often required when reconstructing DICOM data due to the finite field of view of the projection data, where additional axial slices are included on the top and bottom, with zero measured detection events. This transform is included in the system matrix, to model the sharp cutoff at the finite FOV.

class pytomography.transforms.SPECT.SPECTAttenuationTransform(CT)[source]#

Bases: pytomography.transforms.Transform

obj2obj transform used to model the effects of attenuation in SPECT.

Parameters:

CT (torch.tensor) – Tensor of size [batch_size, Lx, Ly, Lz] corresponding to the attenuation coefficient in \({\text{cm}^{-1}}\) at the photon energy corresponding to the particular scan

forward(object_i, ang_idx)#

Forward projection \(A:\mathbb{U} \to \mathbb{U}\) of attenuation correction

Parameters:
  • object_i (torch.tensor) – Tensor of size [batch_size, Lx, Ly, Lz] being projected along axis=1.

  • ang_idx (torch.Tensor) – The projection indices: used to find the corresponding angle in image space corresponding to each projection angle in object_i.

Returns:

Tensor of size [batch_size, Lx, Ly, Lz] such that projection of this tensor along the first axis corresponds to an attenuation corrected projection.

Return type:

torch.tensor

backward(object_i, ang_idx, norm_constant=None)#

Back projection \(A^T:\mathbb{U} \to \mathbb{U}\) of attenuation correction. Since the matrix is diagonal, the implementation is the same as forward projection. The only difference is the optional normalization parameter.

Parameters:
  • object_i (torch.tensor) – Tensor of size [batch_size, Lx, Ly, Lz] being projected along axis=1.

  • ang_idx (torch.Tensor) – The projection indices: used to find the corresponding angle in image space corresponding to each projection angle in object_i.

  • norm_constant (torch.tensor, optional) – A tensor used to normalize the output during back projection. Defaults to None.

Returns:

Tensor of size [batch_size, Lx, Ly, Lz] such that projection of this tensor along the first axis corresponds to an attenuation corrected projection.

Return type:

torch.tensor

class pytomography.transforms.SPECT.SPECTPSFTransform(psf_meta)[source]#

Bases: pytomography.transforms.Transform

obj2obj transform used to model the effects of PSF blurring in SPECT. The smoothing kernel used to apply PSF modeling uses a Gaussian kernel with width \(\sigma\) dependent on the distance of the point to the detector; that information is specified in the PSFMeta parameter.

Parameters:

psf_meta (PSFMeta) – Metadata corresponding to the parameters of PSF blurring

configure(object_meta, image_meta)#

Function used to initalize the transform using corresponding object and image metadata

Parameters:
Return type:

None

compute_kernel_size(radius, axis)#

Function used to compute the kernel size used for PSF blurring. In particular, uses the min_sigmas attribute of PSFMeta to determine what the kernel size should be such that the kernel encompasses at least min_sigmas at all points in the object.

Returns:

The corresponding kernel size used for PSF blurring.

Return type:

int

get_sigma(radius)#

Uses PSF Meta data information to get blurring \(\sigma\) as a function of distance from detector.

Parameters:

radius (float) – The distance from the detector.

Returns:

An array of length Lx corresponding to blurring at each point along the 1st axis in object space

Return type:

array

apply_psf(object, ang_idx)#
forward(object_i, ang_idx)#

Applies the PSF transform \(A:\mathbb{U} \to \mathbb{U}\) for the situation where an object is being detector by a detector at the \(+x\) axis.

Parameters:
  • object_i (torch.tensor) – Tensor of size [batch_size, Lx, Ly, Lz] being projected along its first axis

  • ang_idx (int) – The projection indices: used to find the corresponding angle in image space corresponding to each projection angle in object_i.

Returns:

Tensor of size [batch_size, Lx, Ly, Lz] such that projection of this tensor along the first axis corresponds to n PSF corrected projection.

Return type:

torch.tensor

backward(object_i, ang_idx, norm_constant=None)#

Applies the transpose of the PSF transform \(A^T:\mathbb{U} \to \mathbb{U}\) for the situation where an object is being detector by a detector at the \(+x\) axis. Since the PSF transform is a symmetric matrix, its implemtation is the same as the forward method.

Parameters:
  • object_i (torch.tensor) – Tensor of size [batch_size, Lx, Ly, Lz] being projected along its first axis

  • ang_idx (int) – The projection indices: used to find the corresponding angle in image space corresponding to each projection angle in object_i.

  • norm_constant (torch.tensor, optional) – A tensor used to normalize the output during back projection. Defaults to None.

Returns:

Tensor of size [batch_size, Lx, Ly, Lz] such that projection of this tensor along the first axis corresponds to n PSF corrected projection.

Return type:

torch.tensor

class pytomography.transforms.SPECT.CutOffTransform(image)[source]#

Bases: pytomography.transforms.Transform

im2im transformation used to set pixel values equal to zero at the first and last few z slices. This is often required when reconstructing DICOM data due to the finite field of view of the projection data, where additional axial slices are included on the top and bottom, with zero measured detection events. This transform is included in the system matrix, to model the sharp cutoff at the finite FOV.

Parameters:

image (torch.tensor) – Measured image data.

forward(image)#

Forward projection \(B:\mathbb{V} \to \mathbb{V}\) of the cutoff transform.

Parameters:

image (torch.Tensor) – Tensor of size [batch_size, Ltheta, Lr, Lz] which transform is appplied to

Returns:

Original image, but with certain z-slices equal to zero.

Return type:

torch.tensor

backward(image, norm_constant=None)#

Back projection \(B^T:\mathbb{V} \to \mathbb{V}\) of the cutoff transform. Since this is a diagonal matrix, the implementation is the same as forward projection, but with the optional norm_constant argument.

Parameters:
  • image (torch.Tensor) – Tensor of size [batch_size, Ltheta, Lr, Lz] which transform is appplied to

  • norm_constant (torch.Tensor | None, optional) – A tensor used to normalize the output during back projection. Defaults to None.

Returns:

Original image, but with certain z-slices equal to zero.

Return type:

torch.tensor