The inverse problem for the local geodesic ray transform

• 成果类型: Article
• 署名作者: Uhlmann, Gunther; Vasy, Andras
• 署名单位: University of Washington; University of Washington Seattle; University of Helsinki; Hong Kong University of Science & Technology; Stanford University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0631-7
• 发表日期: 2016
• 页码: 83-120
• 关键词: tensor-fields

摘要

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.