pytomography.algorithms.fbp#

This module contains classes that implement filtered back projection reconstruction algorithms.

Module Contents#

Classes#

FilteredBackProjection

Implementation of filtered back projection reconstruction \(\hat{f} = \frac{\pi}{N_{\text{proj}}} \mathcal{R}^{-1}\mathcal{F}^{-1}\Pi\mathcal{F} g\) where \(N_{\text{proj}}\) is the number of projections, \(\mathcal{R}\) is the 3D radon transform, \(\mathcal{F}\) is the 2D Fourier transform (applied to each projection seperately), and \(\Pi\) is the filter applied in Fourier space, which is by default the ramp filter.
class pytomography.algorithms.fbp.FilteredBackProjection(projections, system_matrix, filter=RampFilter)[source]#

Implementation of filtered back projection reconstruction \(\hat{f} = \frac{\pi}{N_{\text{proj}}} \mathcal{R}^{-1}\mathcal{F}^{-1}\Pi\mathcal{F} g\) where \(N_{\text{proj}}\) is the number of projections, \(\mathcal{R}\) is the 3D radon transform, \(\mathcal{F}\) is the 2D Fourier transform (applied to each projection seperately), and \(\Pi\) is the filter applied in Fourier space, which is by default the ramp filter.

Parameters:

  • projections (torch.Tensor) – projection data \(g\) to be reconstructed

  • system_matrix (SystemMatrix) – system matrix for the imaging system. In FBP, phenomena such as attenuation and PSF should not be implemented in the system matrix

  • filter (Callable, optional) – Additional Fourier space filter (applied after Ramp Filter) used during reconstruction.

__call__(projections)[source]#

Applies reconstruction

Returns:

Reconstructed object prediction

Return type:

torch.tensor