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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 1, Pages 86–103
DOI: https://doi.org/10.33048/semi.2021.18.008 (Mi semr1349) 		 
Computational mathematics

Recovery of a vector field in the cylinder by its jointly known NMR images and ray transforms

E. Yu. Derevtsov, S. V. Maltseva

Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.33048/semi.2021.18.008
Abstract: In the paper we consider a problem of recovering a 3D vector field given in cylinder by means of jointly known nuclear magnetic resonance (NMR) images and ray transforms. The NRM images and 2D longitudinal and transverse ray transforms are known in every plane orthogonal to the cylinder axis. The 3D ray transforms of new type connected with a family of the parallel planes are defined. Simulation confirms the legitimacy and further perspective of the proposed approach.
Keywords: vector field, cylindrical domain, NMR image, ray transform, inversion formula, boundary value problem, numerical simulation.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0011
Russian Foundation for Basic Research 19-51-12008
The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (Project No. 0314-2019-0011) and with partial financial support by the Russian Foundation for Basic Research (RFBR) and the German Science Foundation (DFG) according to the joint German-Russian research project 19-51-12008.
Received November 20, 2020, published February 16, 2021
Bibliographic databases:
Document Type: Article
UDC: 517.983, 519.6
MSC: 65M32
Language: English
Citation: E. Yu. Derevtsov, S. V. Maltseva, “Recovery of a vector field in the cylinder by its jointly known NMR images and ray transforms”, Sib. Èlektron. Mat. Izv., 18:1 (2021), 86–103
Citation in format AMSBIB
\Bibitem{DerMal21}
\by E.~Yu.~Derevtsov, S.~V.~Maltseva
\paper Recovery of a vector field in the cylinder by its jointly known NMR images and ray transforms
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 1
\pages 86--103
\mathnet{http://mi.mathnet.ru/semr1349}
\crossref{https://doi.org/10.33048/semi.2021.18.008}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000620137600001}
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