The inverse problem for the local geodesic ray transform
Differential Geometry
2012-10-09 v1 Analysis of PDEs
Abstract
Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an assumption on the existence of a global foliation by strictly convex hypersurfaces the geodesic X-ray transform is globally injective. In addition we prove stability estimates and propose a layer stripping type algorithm for reconstruction.
Cite
@article{arxiv.1210.2084,
title = {The inverse problem for the local geodesic ray transform},
author = {Gunther Uhlmann and András Vasy},
journal= {arXiv preprint arXiv:1210.2084},
year = {2012}
}
Comments
24 pages, 1 figure