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

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Abstract

A numerical solution to a vector field reconstruction problem is proposed. It is assumed that the field is given in a unit sphere. The approximation of the solenoidal part of the vector field is constructed from ray transforms known over all straight lines parallel to one of the coordinate planes. Numerical simulations confirm that the proposed method yields good results of reconstruction of solenoidal vector fields.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    I. E. Svetov

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    I. E. Svetov

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  1. I. E. Svetov
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Correspondence to I. E. Svetov.

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Original Russian Text © I.E. Svetov, 2012, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2012, Vol. 15, No. 3, pp. 329–344.

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Svetov, I.E. Reconstruction of the solenoidal part of a three-dimensional vector field by its ray transforms along straight lines parallel to coordinate planes. Numer. Analys. Appl. 5, 271–283 (2012). https://doi.org/10.1134/S1995423912030093

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  • DOI: https://doi.org/10.1134/S1995423912030093

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