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Licensed Unlicensed Requires Authentication Published by De Gruyter October 25, 2022

A numerical solution of the dynamic vector tomography problem using the truncated singular value decomposition method

  • Anna P. Polyakova ORCID logo and Ivan E. Svetov ORCID logo EMAIL logo

Abstract

We consider a problem of dynamic 2D vector tomography, i.e. the object under investigation changes during the data acquisition. More precisely, we consider the case when the object motion is a combination of rotation and shifting. The task is then to reconstruct the searched-for vector field by known values of the dynamic ray transforms. In order to solve this dynamic inverse problem, we first study properties of the dynamic ray transforms operators. In particular, the singular value decompositions of the operators are constructed using classic orthogonal polynomials. Following from this study, a numerical algorithm for solving the dynamic problem is proposed based on the truncated singular value decomposition method.

MSC 2010: 65R10; 65R32

Award Identifier / Grant number: FWNF-2022-0009

Award Identifier / Grant number: 19-51-12008

Funding statement: The research is carried out within the framework of the government assignment of the Sobolev Institute of Mathematics, project FWNF-2022-0009, and is partially supported by RFBR and DFG according to the research project 19-51-12008.

Acknowledgements

The authors acknowledge of the assistance of Prof. Dr. Bernadette Hahn-Rigaud for fruitful discussion in preparing the article.

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Received: 2022-03-17
Revised: 2022-06-27
Accepted: 2022-07-17
Published Online: 2022-10-25
Published in Print: 2024-02-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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