This page is a repository for some packages coded for research or teaching topics. Please email for any questions or comments, or cite the appropriate work when using the codes.
5 lectures on Radon and Attenuated Radon transforms
The lectures and codes were designed for the RTG Summer School on X-Ray Tomography and Transport Theory, held at University of Washington, Seattle in June-July 2011.Main topics:
- Fast Fourier Transform and applications.
- The Radon Transform and the Filtered-Backprojection algorithm.
- The attenuated Radon Transform and its inversion.
- Local tomography and limited data problems: recovering singularities
- Cartesian and hyperbolic geometries, fun with FIO's.
GeoXRay (Computation of geodesic X-ray transforms and their inversion)
This code allows to reproduce the experiments of [J13].
Above is an example of a function (left, displayed in gray levels), and its geodesic X-ray transform (right), parameterized in fan-beam coordinates. The inversion process consists in reconstructing the left picture from the right picture.
Main features:
- Computation of geodesic flows for 5 types of scalar metrics and a few types of domains.
- Computation of X-ray transforms for functions and solenoidal vector fields.
- Inversion of both transforms above via Neumann series.