pytomography.transforms#

This module contains transforms; operators that map within the same vector space; such operators are used to build the system matrix. For example, the SPECTAttenuationTransform is an operator \(A:\mathbb{U} \to \mathbb{U}\) which adjusts each voxel in an image based on the probability of it being attenuated before it reaches a detector at the \(+x\) axis. As another example, the CutOffTransform is an operator \(B:\mathbb{V} \to \mathbb{V}\) which sets all pixels in image space equal to zero which exist beyond the detector boundaries. Since operators are often used in reconstruction algorithms, their transpose also must be implemented

Subpackages#

Submodules#

Package Contents#

Classes#

Transform

The parent class for all transforms used in reconstruction (obj2obj, im2im, obj2im). Subclasses must implement the __call__ method.

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.

PETAttenuationTransform

im2im mapping used to model the effects of attenuation in PET.

PETPSFTransform

im2im transform used to model the effects of PSF blurring in PET. The smoothing kernel is assumed to be independent of \(\theta\) and \(z\), but is dependent on \(r\).

class pytomography.transforms.Transform[source]#

The parent class for all transforms used in reconstruction (obj2obj, im2im, obj2im). Subclasses must implement the __call__ method.

Parameters:

device (str) – Pytorch device used for computation

configure(object_meta, image_meta)#

Configures the transform to the object/image metadata. This is done after creating the network so that it can be adjusted to the system matrix.

Parameters:
Return type:

None

abstract forward(x)#

Abstract method; must be implemented in subclasses to apply a correction to an object/image and return it

Parameters:

x (torch.tensor) –

abstract backward(x)#

Abstract method; must be implemented in subclasses to apply a correction to an object/image and return it

Parameters:

x (torch.tensor) –

class pytomography.transforms.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.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.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

class pytomography.transforms.PETAttenuationTransform(CT)[source]#

Bases: pytomography.transforms.Transform

im2im mapping used to model the effects of attenuation in PET.

Parameters:
  • CT (torch.tensor) – Tensor of size [batch_size, Lx, Ly, Lz] corresponding to the attenuation coefficient in \({\text{cm}^{-1}}\) at a photon energy of 511keV.

  • device (str, optional) – Pytorch device used for computation. If None, uses the default device pytomography.device Defaults to None.

configure(object_meta, image_meta)#

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

Parameters:
Return type:

None

forward(image)#

Applies forward projection of attenuation modeling \(B:\mathbb{V} \to \mathbb{V}\) to a 2D PET image.

Parameters:

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

Returns:

Tensor of size [batch_size, Ltheta, Lr, Lz] corresponding to attenuation-corrected image.

Return type:

torch.Tensor

backward(image, norm_constant=None)#

Applies back projection of attenuation modeling \(B^T:\mathbb{V} \to \mathbb{V}\) to a 2D PET image. Since the matrix is diagonal, its the backward implementation is identical to the forward implementation; the only difference is the optional norm_constant which is needed if one wants to normalize the back projection.

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:

Tensor of size [batch_size, Ltheta, Lr, Lz] corresponding to attenuation-corrected image.

Return type:

torch.tensor

class pytomography.transforms.PETPSFTransform(kerns)[source]#

Bases: pytomography.transforms.Transform

im2im transform used to model the effects of PSF blurring in PET. The smoothing kernel is assumed to be independent of \(\theta\) and \(z\), but is dependent on \(r\).

Parameters:

kerns (Sequence[callable]) – A sequence of PSF kernels applied to the Lr dimension of the image with shape [batch_size, Lr, Ltheta, Lz]

configure(object_meta, image_meta)#

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

Parameters:
Return type:

None

construct_matrix()#

Constructs the matrix used to apply PSF blurring.

forward(image)#

Applies the forward projection of PSF modeling \(B:\mathbb{V} \to \mathbb{V}\) to a PET image.

Parameters:

image (torch.tensor]) – Tensor of size [batch_size, Ltheta, Lr, Lz] corresponding to the image

Returns:

Tensor of size [batch_size, Ltheta, Lr, Lz] corresponding to the PSF corrected image.

Return type:

torch.tensor

backward(image, norm_constant=None)#

Applies the back projection of PSF modeling \(B^T:\mathbb{V} \to \mathbb{V}\) to a PET image.

Parameters:
  • image (torch.tensor]) – Tensor of size [batch_size, Ltheta, Lr, Lz] corresponding to the image norm_constant (torch.tensor, optional): A tensor used to normalize the output during back projection. Defaults to None.

  • norm_constant (torch.Tensor | None) –

Returns:

Tensor of size [batch_size, Ltheta, Lr, Lz] corresponding to the PSF corrected image.

Return type:

torch.tensor