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Numerical solution of the problem of reconstructing a potential vector field in the unit ball from its normal Radon transform

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Abstract

A numerical solution is proposed for the problem of reconstructing a potential vector field in the unit ball from the values of the normal Radon transform. The algorithm is based on the method of truncated singular value decomposition. Numerical simulations confirm that the method gives rather good results on reconstructing potential vector fields.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. P. Polyakova & I. E. Svetov

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

    A. P. Polyakova & I. E. Svetov

Authors
  1. A. P. Polyakova
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  2. I. E. Svetov
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Correspondence to A. P. Polyakova.

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Original Russian Text © A.P. Polyakova, I.E. Svetov, 2015, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2015, Vol. XVIII, No. 3, pp. 63–75.

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Polyakova, A.P., Svetov, I.E. Numerical solution of the problem of reconstructing a potential vector field in the unit ball from its normal Radon transform. J. Appl. Ind. Math. 9, 547–558 (2015). https://doi.org/10.1134/S1990478915040110

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  • DOI: https://doi.org/10.1134/S1990478915040110

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