Numerical implementation of geodesic X-ray transforms and their inversion
Differential Geometry
2014-04-17 v2 Analysis of PDEs
Numerical Analysis
Abstract
We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in \cite{Pestov2004,Krishnan2010} are implemented in the case of simple and some non-simple metrics. These numerical tools are also used to better understand and gain intuition about non-simple manifolds, for which injectivity and stability of the corresponding integral geometric problems are still under active study.
Cite
@article{arxiv.1309.6042,
title = {Numerical implementation of geodesic X-ray transforms and their inversion},
author = {François Monard},
journal= {arXiv preprint arXiv:1309.6042},
year = {2014}
}
Comments
23 pages, 11 figures, 2 algorithms. To appear in SIIMS