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.
CITATION STYLE
Uhlmann, G., & Vasy, A. (2016). The inverse problem for the local geodesic ray transform. Inventiones Mathematicae, 205(1), 83–120. https://doi.org/10.1007/s00222-015-0631-7
Mendeley helps you to discover research relevant for your work.