3D pseudo polar Fourier and Radon Transforms

Forward and inverse 3D pseudo polar Fourier transforms and Radon transforms

Description: This package contains functions for 3D pseudo polar Fourier and Radon transforms. More specifically, includes for each a forward transform (i.e. taking an image and computing its 3D ppft/Radon transform) and different methods inversion techniques:
1) Conjugate gradient - An implementation of the inverse PPFT and Radon transform based on conjugate gradients iterations, where each iteration uses the forward and adjoint transforms. This algorithm is slower in practice than those below.
2) Fast convolution based inversion for the PPFT/Radon transforms.
3) Fast convolution based inversion for the PPFT/Radon transforms for GPU computation.
4) Direct inversion - Fast direct inversion for the PPFT/Radon transforms, running time is independent on the input data, no convergence criterion is required by the algorithm.
The algorithms are based on the following papers:
1) A. Averbuch and Y. Shkolnisky, "3D Fourier based discrete Radon transform", Applied and Computational Harmonic Analysis, 15(1):33‐69, 2003.
2) Y. Shkolnisky and S. Golubev, "Fast convolution based inversion of the pseudo‐polar Fourier transform", Technical report.
3) A. Averbuch, G. Shabat and Y. Shkolnisky, "Direct inversion of the 3D pseudo polar Fourier transform. SIAM Journal on Scientific Computing", 38(2), A1100‐A1120, 2016”