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Sibirskii Zhurnal Industrial'noi Matematiki, 2023, Volume 26, Number 4, Pages 125–142
DOI: https://doi.org/10.33048/SIBJIM.2023.26.409 (Mi sjim1265) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Reconstruction of three-dimensional vector fields based on values of normal, longitudinal, and weighted Radon transforms

I. E. Svetov, A. P. Polyakova

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
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DOI: https://doi.org/10.33048/SIBJIM.2023.26.409
Abstract: The paper considers the vector tomography problem of reconstructing a three-dimensional vector field based on the values of unweighted (normal and longitudinal) and weighted Radon transforms. Using the detailed decomposition of vector fields obtained in the paper, connections are established between the unweighted and weighted Radon transforms acting on vector fields and the Radon transform acting on functions. In particular, the kernels of tomographic integral operators acting on vector fields are described. Some statements of tomography problems for the reconstruction of vector fields are considered, and inversion formulas for their solution are obtained.
Keywords: vector tomography, decomposition of vector field, normal Radon transform, longitudinal Radon transform, weighted Radon transform, inversion formula.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0009
The authors thank Isaac Newton Institute for Mathematical Sciences (Cambridge, UK) for its support and hospitality during the “Rich and Nonlinear Tomography—A Multidisciplinary Approach” program in the framework of which work on this paper was carried out. The program is supported by the EPSRC grant no. EP/R014604/1.
Received: 19.05.2023
Revised: 13.09.2023
Accepted: 01.11.2023
English version:
Journal of Applied and Industrial Mathematics, 2023, Volume 17, Issue 4, Pages 842–858
DOI: https://doi.org/10.1134/S1990478923040130
Document Type: Article
UDC: 517.44
Language: Russian
Citation: I. E. Svetov, A. P. Polyakova, “Reconstruction of three-dimensional vector fields based on values of normal, longitudinal, and weighted Radon transforms”, Sib. Zh. Ind. Mat., 26:4 (2023), 125–142; J. Appl. Industr. Math., 17:4 (2023), 842–858
Citation in format AMSBIB
\Bibitem{SvePol23}
\by I.~E.~Svetov, A.~P.~Polyakova
\paper Reconstruction of three-dimensional vector fields based on values of normal, longitudinal, and weighted Radon transforms
\jour Sib. Zh. Ind. Mat.
\yr 2023
\vol 26
\issue 4
\pages 125--142
\mathnet{http://mi.mathnet.ru/sjim1265}
\transl
\jour J. Appl. Industr. Math.
\yr 2023
\vol 17
\issue 4
\pages 842--858
\crossref{https://doi.org/10.1134/S1990478923040130}
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