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Inventiones mathematicae

, Volume 205, Issue 1, pp 83–120 | Cite as

The inverse problem for the local geodesic ray transform

  • Gunther Uhlmann
  • András Vasy
Article

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.

Mathematics Subject Classification

53C65 35R30 35S05 53C21 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Department of MathematicsUniversity of HelsinkiHelsinkiFinland
  3. 3.HKUST Jockey Club Institute for Advanced Study, HKUSTHong KongChina
  4. 4.Department of MathematicsStanford UniversityStanfordUSA

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