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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2012, Volume 12, Issue 3, Pages 73–94 (Mi vngu7)  

This article is cited in 13 scientific papers (total in 13 papers)

An Application of the SVD-Method to the Problem of Integral Geometry of 2-Tensor Fields

E. Yu. Derevtsovab, A. P. Polyakovab

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
References:
Abstract: A problem of integral geometry consisting in determination of a given in unit disk symmetric 2-tensor field by its known ray transforms is considered. Singular value decompositions (SVD) of the operators of longitudinal, transverse and mixed ray transforms that are the integrals of projections of a field at a line of integration are constructed. The results are based essentially on a theorem of a tensor field decomposition and its representation through potentials. The obtained singular value decompositions are constructive and are foundations for the algorithms of a tensor field reconstruction by its known ray transforms.
Keywords: tensor field, integral geometry, tensor tomography, ray transform.
Received: 18.01.2012
English version:
Journal of Mathematical Sciences, 2014, Volume 202, Issue 1, Pages 50–71
DOI: https://doi.org/10.1007/s10958-014-2033-6
Document Type: Article
UDC: 517.983:519.642
Language: Russian
Citation: E. Yu. Derevtsov, A. P. Polyakova, “An Application of the SVD-Method to the Problem of Integral Geometry of 2-Tensor Fields”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 12:3 (2012), 73–94; J. Math. Sci., 202:1 (2014), 50–71
Citation in format AMSBIB
\Bibitem{DerPol12}
\by E.~Yu.~Derevtsov, A.~P.~Polyakova
\paper An Application of the SVD-Method to the Problem of Integral Geometry of 2-Tensor Fields
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2012
\vol 12
\issue 3
\pages 73--94
\mathnet{http://mi.mathnet.ru/vngu7}
\transl
\jour J. Math. Sci.
\yr 2014
\vol 202
\issue 1
\pages 50--71
\crossref{https://doi.org/10.1007/s10958-014-2033-6}
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  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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    References:54
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