This article is cited in 2 papers

Computational mathematics

Approximate inversion of operators of two-dimensional vector tomography

I. E. Svetov^ab, S. V. Maltseva^abc, A. P. Polyakova<sup>ab

a</sup> Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Novosibirsk state university, st. Pirogova, 2, 630090, Novosibirsk, Russia
^c Lavrentyev Institute of Hydrodynamics, pr. Lavrentyeva, 15, 630090, Novosibirsk, Russia

Abstract: We propose two approaches for numerical solution of reconstruction problem of a vector field in an unit disk from the known values of longitudinal and transverse ray transforms. The algorithms are based on the method of approximate inverse. Numerical simulations show that the proposed algorithms yield good results of reconstruction of vector fields.

Keywords: vector tomography, method of approximate inverse, longitudinal ray transform, transverse ray transform, Radon transform, solenoidal vector field, potential vector field, potential, numerical simulation.

UDC: 514.8:517.983:519.6

MSC: 44A30

Received May 19, 2016, published August 12, 2016

DOI: 10.17377/semi.2016.13.048