This article is cited in 5 papers

Computational mathematics

Approximate solution of two-dimensional 2-tensor tomography problem using truncated singular value decomposition

I. E. Svetov^ab, A. P. Polyakova<sup>ba

a</sup> Novosibirsk State University, st. Pirogova, 2, 630090, Novosibirsk, Russia
^b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: We propose a numerical solution of reconstruction problem of 2-tensor field in a unit disk from its known values of the ray transforms. The algorithm is based on the method of truncated singular value decomposition. Numerical simulations demonstrate an efficiency of the proposed approach. In addition, we compare proposed algorithm with an algorithm based on the least squares method where we use a finite basis consisting of $B$-splines as basis functions.

Keywords: 2-tensor tomography, solenoidal field, potential field, approximation, ray transforms, truncated singular value decomposition, orthogonal polynomials, least squares method, $B$-splines.

Received March 30, 2015, published September 9, 2015

DOI: 10.17377/semi.2015.12.041