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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 607–623
DOI: https://doi.org/10.17377/semi.2016.13.048 (Mi semr698) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Computational mathematics

Approximate inversion of operators of two-dimensional vector tomography

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

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk state university, st. Pirogova, 2, 630090, Novosibirsk, Russia
c Lavrentyev Institute of Hydrodynamics, pr. Lavrentyeva, 15, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/semi.2016.13.048
Abstract: We propose two approaches for numerical solution of reconstruction problem of a vector field in an unit disk from the known values of longitudinal and transverse ray transforms. The algorithms are based on the method of approximate inverse. Numerical simulations show that the proposed algorithms yield good results of reconstruction of vector fields.
Keywords: vector tomography, method of approximate inverse, longitudinal ray transform, transverse ray transform, Radon transform, solenoidal vector field, potential vector field, potential, numerical simulation.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0314-2015-0010
Russian Foundation for Basic Research 14-01-31491-мол_а
Received May 19, 2016, published August 12, 2016
Document Type: Article
UDC: 514.8:517.983:519.6
MSC: 44A30
Language: Russian
Citation: I. E. Svetov, S. V. Maltseva, A. P. Polyakova, “Approximate inversion of operators of two-dimensional vector tomography”, Sib. Èlektron. Mat. Izv., 13 (2016), 607–623
Citation in format AMSBIB
\Bibitem{SveMalPol16}
\by I.~E.~Svetov, S.~V.~Maltseva, A.~P.~Polyakova
\paper Approximate inversion of operators of two-dimensional vector tomography
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 607--623
\mathnet{http://mi.mathnet.ru/semr698}
\crossref{https://doi.org/10.17377/semi.2016.13.048}
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