Numerical Implementation of Geodesic X-Ray Transforms and Their Inversion
Numerical Implementation of Geodesic X-Ray Transforms and Their Inversion
复制标题
测地X射线变换及其反演的数值实现
DOI：
10.1137/130938657
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
F. Monard
中科院分区：
文献类型：
--
作者：
F. Monard
我们给出了测地线射线变换及其在二维黎曼流形上对函数和无散向量场的反演的一种数值实现。对于每个问题，先前在\(\cite{Pestov2004,Krishnan2010}\)中推导的反演公式在简单度量以及一些非简单度量的情形下得以实现。这些数值工具还被用于更好地理解非简单流形并获得相关直觉，对于非简单流形，相应积分几何问题的单射性和稳定性仍在积极研究中。
We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in \cite{Pestov2004,Krishnan2010} are implemented in the case of simple and some non-simple metrics. These numerical tools are also used to better understand and gain intuition about non-simple manifolds, for which injectivity and stability of the corresponding integral geometric problems are still under active study.