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Sib. Zh. Vychisl. Mat., 2010, Volume 13, Number 2, Pages 183–199 (Mi sjvm276)  

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.

Full text: PDF file (596 kB)
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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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet
    2. I. E. Svetov, A. P. Polyakova, “Sravnenie dvukh algoritmov chislennogo resheniya zadachi dvumernoi vektornoi tomografii”, Sib. elektron. matem. izv., 10 (2013), 90–108  mathnet
    3. 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  crossref  mathscinet  isi  elib  scopus
    4. 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  crossref  isi
    5. 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  crossref  mathscinet  zmath  isi  scopus
    6. 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  mathnet  crossref  crossref  elib
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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