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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2012, Volume 12, Issue 3, Pages 73–94
(Mi vngu7)
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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
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
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
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Abstract page: | 281 | Full-text PDF : | 74 | References: | 54 | First page: | 4 |
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