Matrix-free X-ray tomography

This page contains the computational Matlab files related to the book
 Linear and Nonlinear Inverse Problems with Practical Applications
written by Jennifer Mueller and Samuli Siltanen and published by SIAM in 2012.

You can order the book at the SIAM webshop.

Go to master page

Here we solve tomographic problems without constructing the measurement matrix A at all.

Simulate tomographic data without inverse crime

This routine uses the radon.m function of Matlab's Image processing toolbox to create a sinogram:

XRA_NoCrimeData_comp.m

Compute reconstruction using filtered back-projection

XRB_FBP_comp.m

Compute reconstruction using matrix-free iterative Tikhonov regularization

XRC_Tikhonov_comp.m, XRC_Tikhonov_plot.m

Compute reconstruction using matrix-free iterative (approximate) total variation regularization

Here are the main computation and plot routines:

XRD_aTV_comp.m, XRD_aTV_plot.m

You will also need these files:

XR_aTV_feval.m, XR_aTV_fgrad.m, XR_aTV_grad.m, XR_aTV.m, XR_misfit_grad.m, XR_misfit.m