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Sibirskii Zhurnal Industrial'noi Matematiki, 2019, Volume 22, Number 1, Pages 104–115
DOI: https://doi.org/10.33048/sibjim.2019.22.110 (Mi sjim1036) 		 
This article is cited in 5 scientific papers (total in 5 papers)

The method of approximate inverse for ray transform operators on two-dimensional symmetric $m$-tensor fields

I. E. Svetovab, A. P. Polyakovaab, S. V. Maltsevaabc

a Sobolev Institute of Mathematics SB RAS, pr. Akad. Koptyuga 4, 630090 Novosibirsk
b Novosibirsk State University, ul. Pirogova 2, 630090 Novosibirsk
c Lavrentyev Institute of Hydrodynamics SB RAS, pr. Akad. Lavrentyeva 15, 630090 Novosibirsk
Full-text PDF (265 kB) Citations (5)
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DOI: https://doi.org/10.33048/sibjim.2019.22.110
Abstract: Two approaches are proposed for recovering a symmetric $m$-tensor field in a unit disk from the given values of ray transforms. The approaches are based on the method of approximate inverse. The first approach allows us to reconstruct all components of the tensor field, while the second recovers the potentials of the solenoidal part and $m$ potential parts of the tensor field.
Keywords: tensor tomography, method of approximate inverse, adjoint operator, ray transform, Radon transform, tensor field, potential.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences I.1.5 (проект 0314-2016-0011)
Russian Foundation for Basic Research 18-01-00057_а
Received: 09.06.2018
Revised: 24.10.2018
Accepted: 15.12.2018
English version:
Journal of Applied and Industrial Mathematics, 2019, Volume 13, Issue 1, Pages 157–167
DOI: https://doi.org/10.1134/S1990478919010162
Bibliographic databases:
Document Type: Article
UDC: 517.98:519.677
Language: Russian
Citation: I. E. Svetov, A. P. Polyakova, S. V. Maltseva, “The method of approximate inverse for ray transform operators on two-dimensional symmetric $m$-tensor fields”, Sib. Zh. Ind. Mat., 22:1 (2019), 104–115; J. Appl. Industr. Math., 13:1 (2019), 157–167
Citation in format AMSBIB
\Bibitem{SvePolMal19}
\by I.~E.~Svetov, A.~P.~Polyakova, S.~V.~Maltseva
\paper The method of approximate inverse for ray transform operators on two-dimensional symmetric $m$-tensor fields
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 1
\pages 104--115
\mathnet{http://mi.mathnet.ru/sjim1036}
\crossref{https://doi.org/10.33048/sibjim.2019.22.110}
\elib{https://elibrary.ru/item.asp?id=38683430}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 1
\pages 157--167
\crossref{https://doi.org/10.1134/S1990478919010162}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85064909425}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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