A numerical solution of the dynamic vector tomography problem using the truncated singular value decomposition method Full article
| Journal |
Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219 , E-ISSN: 1569-3945 |
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| Output data | Year: 2024, Volume: 32, Number: 1, DOI: 10.1515/jiip-2022-0019 | ||
| Tags | Dynamic vector tomography; longitudinal ray transform; orthogonal polynomial; singular value decomposition; transverse ray transform | ||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
| 2 | Russian Foundation for Basic Research | 19-51-12008 |
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.
Cite:
Polyakova A.P.
, Svetov I.E.
A numerical solution of the dynamic vector tomography problem using the truncated singular value decomposition method
Journal of Inverse and Ill-Posed Problems. 2024. V.32. N1. DOI: 10.1515/jiip-2022-0019 WOS Scopus РИНЦ OpenAlex
A numerical solution of the dynamic vector tomography problem using the truncated singular value decomposition method
Journal of Inverse and Ill-Posed Problems. 2024. V.32. N1. DOI: 10.1515/jiip-2022-0019 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Mar 17, 2022 |
| Accepted: | Jul 17, 2022 |
| Published online: | Oct 25, 2022 |
| Published print: | Feb 1, 2024 |
Identifiers:
| Web of science: | WOS:000871634700001 |
| Scopus: | 2-s2.0-85141132489 |
| Elibrary: | 57963790 |
| OpenAlex: | W4307282813 |