Reconstruction of the singular support of a tensor field given in a refracting medium by its ray transform

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• 作者：E. Yu. Derevtsov ; S. V. Maltseva
• 关键词：tomography ; tensor field ; function discontinuity ; singular support ; refraction ; ray transform ; back ; projection operator ; tensor analysis
• 刊名：Journal of Applied and Industrial Mathematics
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：9
• 期：4
• 页码：447-460
• 全文大小：1,378 KB
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• 作者单位：E. Yu. Derevtsov (1) (2)
  S. V. Maltseva (1) (2) (3)
  
  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
  3. Lavrent鈥檈v Institute of Hydrodynamics, pr. Akad. Lavrent鈥檈va 15, Novosibirsk, 630090, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1990-4797

文摘

We propose some approaches for numerically solving the problem of reconstructing the singular support of a symmetric tensor field, given in a refracting medium, by its known ray transform. To solve the problem, we use the back-projection operators that act on the ray transforms and the tensor analysis methods on Riemannian manifolds. We construct the operators of the medium inhomogeneity indicator that allow us to identify the sets of points of the singular support of the scalar, vector, and tensor fields. We propose and implement algorithms for solving the problem under study. Keywords tomography tensor field function discontinuity singular support refraction ray transform back-projection operator tensor analysis