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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2014, Volume 11, Pages 833–856 (Mi semr527)  
This article is cited in 2 scientific papers (total in 2 papers)

Computational mathematics

A numerical inversion of the ray transform operator in refraction tomography

E. Yu. Derevtsovab, S. V. Maltsevaab, I. E. Svetovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
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Abstract: We suggest an approach to an approximate inversion of the ray transform operator acting on functions given in Riemannian domain. We construct an inversion algorithm with usage of ray and beam transforms, back-projection operator and Fourier transform. The algorithm is investigated by numerical experiments. The results of simulation are compared with results of the other algorithm constructed on the base of least square method by means of $B$-splines.
Keywords: tomography, refraction, ray transform, back-projection operator, inversion formula, Fourier transform, least square method, $B$-splines.
Received June 16, 2014, published November 20, 2014
Document Type: Article
UDC: 514.8, 517.983, 519.6
MSC: 44A30
Language: Russian
Citation: E. Yu. Derevtsov, S. V. Maltseva, I. E. Svetov, “A numerical inversion of the ray transform operator in refraction tomography”, Sib. Èlektron. Mat. Izv., 11 (2014), 833–856
Citation in format AMSBIB
\Bibitem{DerMalSve14}
\by E.~Yu.~Derevtsov, S.~V.~Maltseva, I.~E.~Svetov
\paper A numerical inversion of the ray transform operator in refraction tomography
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 833--856
\mathnet{http://mi.mathnet.ru/semr527}
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