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This article is cited in 6 scientific papers (total in 6 papers)
Reconstruction of 2-tensor fields, given in a unit circle, by their ray transforms based on LSM with $B$-splines
I. E. Svetovab, A. P. Polyakovab
a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University, Novosibirsk
Abstract:
The numerical method for solving a tensor tomography problem of reconstructing a symmetric 2-tensor field, given in a unit circle, is offered. Potential and (or) solenoidal part of the desired field with fixed properties on the boundary are found from transverse and (or) longitudinal ray transforms, calculated along the straight lines crossing the support of the field. The solution is sought by means of the least-squares method with the use, as approximating sequence, of local bases, constructed on the basis of $B$-splines.
Key words:
tensor tomography, potential field, solenoidal field, least-squares method, $B$-splines, approximation, fast Fourier transform.
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English version:
Numerical Analysis and Applications, 2010, 3:2, 151–164
UDC:
514.8+517.983+519.6
Received: 15.05.2009
Revised: 13.07.2009
Citation:
I. E. Svetov, A. P. Polyakova, “Reconstruction of 2-tensor fields, given in a unit circle, by their ray transforms based on LSM with $B$-splines”, Sib. Zh. Vychisl. Mat., 13:2 (2010), 183–199; Num. Anal. Appl., 3:2 (2010), 151–164
Citation in format AMSBIB
\Bibitem{SvePol10}
\by I.~E.~Svetov, A.~P.~Polyakova
\paper Reconstruction of 2-tensor fields, given in a~unit circle, by their ray transforms based on LSM with $B$-splines
\jour Sib. Zh. Vychisl. Mat.
\yr 2010
\vol 13
\issue 2
\pages 183--199
\mathnet{http://mi.mathnet.ru/sjvm276}
\transl
\jour Num. Anal. Appl.
\yr 2010
\vol 3
\issue 2
\pages 151--164
\crossref{https://doi.org/10.1134/S1995423910020047}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77953522873}
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http://mi.mathnet.ru/eng/sjvm276 http://mi.mathnet.ru/eng/sjvm/v13/i2/p183
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Russian articles,
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This publication is cited in the following articles:
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I. E. Svetov, “Vosstanovlenie solenoidalnykh $2$-tenzornykh polei, zadannykh v edinichnom kruge, po ikh prodolnym luchevym preobrazovaniyam”, Sib. elektron. matem. izv., 7 (2010), 139–149
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I. E. Svetov, A. P. Polyakova, “Sravnenie dvukh algoritmov chislennogo resheniya zadachi dvumernoi vektornoi tomografii”, Sib. elektron. matem. izv., 10 (2013), 90–108
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Svetov I.E. Derevtsov E.Yu. Volkov Yu.S. Schuster T., “A Numerical Solver Based on B-Splines for 2D Vector Field Tomography in a Refracting Medium”, Math. Comput. Simul., 97 (2014), 207–223
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Polyakova A.P., Svetov I.E., “Numerical Solution of Reconstruction Problem of a Potential Symmetric 2-Tensor Field in a Ball From Its Normal Radon Transform”, Sib. Electron. Math. Rep., 13 (2016), 154–174
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Derevtsov E.Yu. Louis A.K. Maltseva S.V. Polyakova A.P. Svetov I.E., “Numerical Solvers Based on the Method of Approximate Inverse For 2D Vector and 2-Tensor Tomography Problems”, Inverse Probl., 33:12 (2017), 124001
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I. E. Svetov, A. P. Polyakova, S. V. Maltseva, “The method of approximate inverse for ray transform operators on two-dimensional symmetric $m$-tensor fields”, J. Appl. Industr. Math., 13:1 (2019), 157–167
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