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Sibirskii Zhurnal Industrial'noi Matematiki, 2015, Volume 18, Number 3, Pages 63–75
DOI: https://doi.org/10.17377/sibjim.2015.18.307 (Mi sjim895) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Numerical solution of reconstruction problem of a potential vector field in a ball from its normal Radon transform

A. P. Polyakovaab, I. E. Svetovab

a Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk
b Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
Full-text PDF (1053 kB) Citations (11)
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DOI: https://doi.org/10.17377/sibjim.2015.18.307
Abstract: We propose a numerical solution of reconstruction problem of a potential vector field in a ball from the known values of the normal Radon transform. The algorithm is based on the method of truncated singular value decomposition. Numerical simulations confirm that the proposed method yields good results of reconstruction of potential vector fields.
Keywords: vector tomography, potential vector field, approximation, normal Radon transform, truncated singular value decomposition, orthogonal polynomials.
Received: 11.03.2015
English version:
Journal of Applied and Industrial Mathematics, 2015, Volume 9, Issue 4, Pages 547–558
DOI: https://doi.org/10.1134/S1990478915040110
Bibliographic databases:
Document Type: Article
UDC: 514.8+517.983+519.6
Language: Russian
Citation: A. P. Polyakova, I. E. Svetov, “Numerical solution of reconstruction problem of a potential vector field in a ball from its normal Radon transform”, Sib. Zh. Ind. Mat., 18:3 (2015), 63–75; J. Appl. Industr. Math., 9:4 (2015), 547–558
Citation in format AMSBIB
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\by A.~P.~Polyakova, I.~E.~Svetov
\paper Numerical solution of reconstruction problem of a~potential vector field in a~ball from its normal Radon transform
\jour Sib. Zh. Ind. Mat.
\yr 2015
\vol 18
\issue 3
\pages 63--75
\mathnet{http://mi.mathnet.ru/sjim895}
\crossref{https://doi.org/10.17377/sibjim.2015.18.307}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3549841}
\elib{https://elibrary.ru/item.asp?id=23877192}
\transl
\jour J. Appl. Industr. Math.
\yr 2015
\vol 9
\issue 4
\pages 547--558
\crossref{https://doi.org/10.1134/S1990478915040110}
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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