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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2011, Volume 14, Number 1, Pages 29–46 (Mi sjvm424)  
This article is cited in 15 scientific papers (total in 15 papers)

Reconstruction of vector fields and their singularities from ray transforms

E. Yu. Derevtsovab, V. V. Pickalovc

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk
c Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (1385 kB) Citations (15)
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Abstract: In this paper, numerical methods for reconstruction of the singular support of a vector field from its known longitudinal and (or) transverse ray transforms are proposed. Apart from a modification for the Vainberg operator, we use integral operators of angular moments and back projections as well as differential operators of tensor analysis for solving the problem. Results of numerical simulation for reconstructing discontinuous vector fields and with discontinuities in the derivatives are presented. Visualization of their singular support is shown.
Key words: vector tomography, tensor field, Radon transform, ray transform, angular moment, back projection, inversion formulas, singular support, visualization.
Received: 01.06.2010
Revised: 15.06.2010
English version:
Numerical Analysis and Applications, 2011, Volume 4, Issue 1, Pages 21–35
DOI: https://doi.org/10.1134/S1995423911010034
Bibliographic databases:
Document Type: Article
UDC: 517.98+519.677
Language: Russian
Citation: E. Yu. Derevtsov, V. V. Pickalov, “Reconstruction of vector fields and their singularities from ray transforms”, Sib. Zh. Vychisl. Mat., 14:1 (2011), 29–46; Num. Anal. Appl., 4:1 (2011), 21–35
Citation in format AMSBIB
\Bibitem{DerPic11}
\by E.~Yu.~Derevtsov, V.~V.~Pickalov
\paper Reconstruction of vector fields and their singularities from ray transforms
\jour Sib. Zh. Vychisl. Mat.
\yr 2011
\vol 14
\issue 1
\pages 29--46
\mathnet{http://mi.mathnet.ru/sjvm424}
\transl
\jour Num. Anal. Appl.
\yr 2011
\vol 4
\issue 1
\pages 21--35
\crossref{https://doi.org/10.1134/S1995423911010034}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952477299}
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Sibirskii Zhurnal Vychislitel'noi Matematiki
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