Аннотация:
A problem of 3D 2-tensor field potential part reconstruction by the known value of its normal Radon transform is considered. A singular value decomposition of the operator is constructed for solving the problem. Basic fields are constructed with the use of Jacobi polynomials, Gegenbauer polynomials, and spherical harmonics.
Ключевые слова:
symmetric tensor field, potential field, potential, normal Radon transform, singular value decomposition of an operator, system of orthogonal polynomials.
The research was carried out within the state assignment for Sobolev Institute of Mathematics SB RAS (project
№-0314-2019-0011) and with a partial support of RFBR and DFG according to the project 19-51-12008.
Поступила17 мая 2021 г., опубликована 7 декабря 2021 г.
Образец цитирования:
A. P. Polyakova, “Singular value decomposition of a normal Radon transform operator acting on 3D symmetric 2-tensor fields”, Сиб. электрон. матем. изв., 18:2 (2021), 1572–1595
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\by A.~P.~Polyakova
\paper Singular value decomposition of a normal Radon transform operator acting on 3D symmetric 2-tensor fields
\jour Сиб. электрон. матем. изв.
\yr 2021
\vol 18
\issue 2
\pages 1572--1595
\mathnet{http://mi.mathnet.ru/semr1461}
\crossref{https://doi.org/10.33048/semi.2021.18.117}
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/semr1461
https://www.mathnet.ru/rus/semr/v18/i2/p1572
Эта публикация цитируется в следующих 2 статьяx:
Ivan E Svetov, Anna P Polyakova, “Inversion of generalized Radon transforms acting on 3D vector and symmetric tensor fields”, Inverse Problems, 40:1 (2024), 015009
И. Е. Светов, А. П. Полякова, “Разложение симметричных тензорных полей в R3”, Сиб. журн. индустр. матем., 26:1 (2023), 161–178; I. E. Svetov, A. P. Polyakova, “Decomposition of symmetric tensor fields in R3”, J. Appl. Industr. Math., 17:1 (2023), 199–212
Цитирование в формате AMSBIB
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