Numerical implementation of geodesic X-ray transforms and their\n inversion

2013/09/24 by François Monard, Monard, François · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1309.6042

openalex publication_date 2013/09/24 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We present a numerical implementation of the geodesic ray transform and its\ninversion over functions and solenoidal vector fields on two-dimensional\nRiemannian manifolds. For each problem, inversion formulas previously derived\nin citePestov2004,Krishnan2010 are implemented in the case of simple and\nsome non-simple metrics. These numerical tools are also used to better\nunderstand and gain intuition about non-simple manifolds, for which injectivity\nand stability of the corresponding integral geometric problems are still under\nactive study.\n

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