A. P. Polyakova, I. E. Svetov, “Numerical solution of reconstruction problem of a potential vector field in a ball from its normal Radon transform”, Sib. Zh. Ind. Mat., 18:3 (2015), 63–75; J. Appl. Industr. Math., 9:4 (2015), 547

Sibirskii Zhurnal Industrial'noi Matematiki

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Sib. Zh. Ind. Mat.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Sibirskii Zhurnal Industrial'noi Matematiki, 2015, Volume 18, Number 3, Pages 63–75
DOI: https://doi.org/10.17377/sibjim.2015.18.307 (Mi sjim895)

This article is cited in 11 scientific papers (total in 11 papers)

Numerical solution of reconstruction problem of a potential vector field in a ball from its normal Radon transform

A. P. Polyakova^ab, I. E. Svetov^ab

^a Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk
^b Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk

Full-text PDF (1053 kB) Citations (11)

References:

PDF

HTML

DOI: https://doi.org/10.17377/sibjim.2015.18.307

Abstract: We propose a numerical solution of reconstruction problem of a potential vector field in a ball from the known values of the normal Radon transform. The algorithm is based on the method of truncated singular value decomposition. Numerical simulations confirm that the proposed method yields good results of reconstruction of potential vector fields.

Keywords: vector tomography, potential vector field, approximation, normal Radon transform, truncated singular value decomposition, orthogonal polynomials.

Received: 11.03.2015

English version:
Journal of Applied and Industrial Mathematics, 2015, Volume 9, Issue 4, Pages 547–558
DOI: https://doi.org/10.1134/S1990478915040110

Bibliographic databases:

Document Type: Article

UDC: 514.8+517.983+519.6

Language: Russian

Citation: A. P. Polyakova, I. E. Svetov, “Numerical solution of reconstruction problem of a potential vector field in a ball from its normal Radon transform”, Sib. Zh. Ind. Mat., 18:3 (2015), 63–75; J. Appl. Industr. Math., 9:4 (2015), 547–558

Citation in format AMSBIB

\Bibitem{PolSve15}

\by A.~P.~Polyakova, I.~E.~Svetov

\paper Numerical solution of reconstruction problem of a~potential vector field in a~ball from its normal Radon transform

\jour Sib. Zh. Ind. Mat.

\yr 2015

\vol 18

\issue 3

\pages 63--75

\mathnet{http://mi.mathnet.ru/sjim895}

\crossref{https://doi.org/10.17377/sibjim.2015.18.307}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3549841}

\elib{https://elibrary.ru/item.asp?id=23877192}

\transl

\jour J. Appl. Industr. Math.

\yr 2015

\vol 9

\issue 4

\pages 547--558

\crossref{https://doi.org/10.1134/S1990478915040110}

Linking options:

https://www.mathnet.ru/eng/sjim895

https://www.mathnet.ru/eng/sjim/v18/i3/p63

This publication is cited in the following 11 articles:

L Kunyansky, E McDugald, B Shearer, “Weighted Radon transforms of vector fields, with applications to magnetoacoustoelectric tomography”, Inverse Problems, 39:6 (2023), 065014
Anna P. Polyakova, Ivan E. Svetov, “A numerical solution of the dynamic vector tomography problem using the truncated singular value decomposition method”, Journal of Inverse and Ill-posed Problems, 2022
Polyakova A.P., “Singular Value Decomposition of a Normal Radon Transform Operator Acting on 3D Symmetric 2-Tensor Fields”, Sib. Electron. Math. Rep., 18:2 (2021), 1572–1595
I E Svetov, A P Polyakova, “The method of approximate inverse for the normal Radon transform operator”, J. Phys.: Conf. Ser., 1715:1 (2021), 012048
A P Polyakova, I E Svetov, “On a singular value decomposition of the normal Radon transform operator acting on 3D 2-tensor fields”, J. Phys.: Conf. Ser., 1715:1 (2021), 012041
Anna P. Polyakova, Ivan E. Svetov, Bernadette N. Hahn, Lecture Notes in Computer Science, 11974, Numerical Computations: Theory and Algorithms, 2020, 446
Ivan E. Svetov, Svetlana V. Maltseva, Alfred K. Louis, Lecture Notes in Computer Science, 11974, Numerical Computations: Theory and Algorithms, 2020, 487
Shidong Sun, Lei Qin, Hongwei Ren, “Effect of Different Electrode Numbers on the Image Quality of Concrete Damage in Electrical Resistance Tomography”, IOP Conf. Ser.: Earth Environ. Sci., 283:1 (2019), 012005
L. Liu, Z. Y. Fang, Y. P. Wu, X. P. Lai, P. Wang, K.-I. Song, “Experimental investigation of solid-liquid two-phase flow in cemented rock-tailings backfill using Electrical Resistance Tomography”, Constr. Build. Mater., 175 (2018), 267–276
A. P. Polyakova, I. E. Svetov, “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
I. E. Svetov, S. V. Maltseva, A. P. Polyakova, “Approximate inversion of operators of two-dimensional vector tomography”, Sib. Electron. Math. Rep., 13 (2016), 607–623

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Сибирский журнал индустриальной математики

Statistics & downloads:
Abstract page:	265
Full-text PDF :	144
References:	55
First page:	11

Registration to the website

Logotypes