I. E. Svetov, “Reconstruction of solenoidal part of a three-dimensional vector field by its ray transforms along straight lines, parallel to the coordinate planes”, Sib. Zh. Vychisl. Mat., 15:3 (2012), 329–344; Num. Anal. Appl., 5:3 (2012), 271

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2012, Volume 15, Number 3, Pages 329–344 (Mi sjvm484)

This article is cited in 12 scientific papers (total in 12 papers)

Reconstruction of solenoidal part of a three-dimensional vector field by its ray transforms along straight lines, parallel to the coordinate planes

I. E. Svetov^ab

^a Novosibirsk State University, Novosibirsk
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Full-text PDF (659 kB) Citations (12)

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Abstract: The numerical solution of a vector field reconstruction problem is offered. It is assumed that a field is given in a unit ball. The approximation of the solenoidal part of the vector field is constructed from ray transforms known over all the straight lines parallel to one of the coordinate planes. Good results of reconstruction of solenoidal vector fields by the numerical simulations are proposed.

Key words: vector tomography, solenoidal field, approximation, inversion formula, ray transform, fast Fourier transform.

Received: 21.04.2011
Revised: 15.06.2011

English version:
Numerical Analysis and Applications, 2012, Volume 5, Issue 3, Pages 271–283
DOI: https://doi.org/10.1134/S1995423912030093

Bibliographic databases:

Document Type: Article

UDC: 514.8+517.983+519.6

Language: Russian

Citation: I. E. Svetov, “Reconstruction of solenoidal part of a three-dimensional vector field by its ray transforms along straight lines, parallel to the coordinate planes”, Sib. Zh. Vychisl. Mat., 15:3 (2012), 329–344; Num. Anal. Appl., 5:3 (2012), 271–283

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sjvm484

https://www.mathnet.ru/eng/sjvm/v15/i3/p329

This publication is cited in the following 12 articles:

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
Derevtsov E.Yu. Maltseva V S., “Recovery of a Vector Field in the Cylinder By Its Jointly Known Nmr Images and Ray Transforms”, Sib. Electron. Math. Rep., 18 (2021), 86–103
Mishra R.K., Sahoo S.K., “Injectivity and Range Description of Integral Moment Transforms Over M-Tensor Fields in R-N”, SIAM J. Math. Anal., 53:1 (2021), 253–278
A K Louis, S V Maltseva, A P Polyakova, T Schuster, I E Svetov, “On solving the slice-by-slice three-dimensional 2-tensor tomography problems using the approximate inverse method”, J. Phys.: Conf. Ser., 1715:1 (2021), 012036
Mishra R.K., “Full Reconstruction of a Vector Field From Restricted Doppler and First Integral Moment Transforms in R-N”, J. Inverse Ill-Posed Probl., 28:2 (2020), 173–184
Polyakova A.P. Svetov I.E. Hahn B.N., “the Singular Value Decomposition of the Operators of the Dynamic Ray Transforms Acting on 2D Vector Fields”, Numerical Computations: Theory and Algorithms, Pt II, Lecture Notes in Computer Science, 11974, ed. Sergeyev Y. Kvasov D., Springer International Publishing Ag, 2020, 446–453
Svetov I.E., Maltseva V S., Louis A.K., “the Method of Approximate Inverse in Slice-By-Slice Vector Tomography Problems”, Numerical Computations: Theory and Algorithms, Pt II, Lecture Notes in Computer Science, 11974, eds. Sergeyev Y., Kvasov D., Springer International Publishing Ag, 2020, 487–494
Svetov I.E., “the Method of Approximate Inverse For the Radon Transform Operator Acting on Functions and For the Normal Radon Transform Operators Acting on Vector and Symmetric 2-Tensor Fields in R-3”, Sib. Electron. Math. Rep., 17 (2020), 1073–1087
Maltseva V S., Svetov I.E., Polyakova A.P., “Reconstruction of a Function and Its Singular Support in a Cylinder By Tomographic Data”, Eurasian J. Math. Comput. Appl., 8:2 (2020), 86–97
Leweke S., Michel V., Schneider N., “Vectorial Slepian Functions on the Ball”, Numer. Funct. Anal. Optim., 39:11 (2018), 1120–1152
I. E. Svetov, S. V. Maltseva, A. P. Polyakova, “Priblizhennoe obraschenie operatorov dvumernoi vektornoi tomografii v $\mathbb{R}^2$”, Sib. elektron. matem. izv., 13 (2016), 607–623
A. P. Polyakova, I. E. Svetov, “Numerical solution of reconstruction problem of a potential vector field in a ball from its normal Radon transform”, J. Appl. Industr. Math., 9:4 (2015), 547–558

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

Sibirskii Zhurnal Vychislitel'noi Matematiki

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