I. E. Svetov, A. P. Polyakova, S. V. Maltseva, “The method of approximate inverse for ray transform operators on two-dimensional symmetric <nobr>$m$</nobr>-tensor fields”, Sib. Zh. Ind. Mat., 2019, Volume 22, Number 1,Pages <nobr>104

This article is cited in 5 papers

The method of approximate inverse for ray transform operators on two-dimensional symmetric $m$-tensor fields

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

^a Sobolev Institute of Mathematics SB RAS, pr. Akad. Koptyuga 4, 630090 Novosibirsk
^b Novosibirsk State University, ul. Pirogova 2, 630090 Novosibirsk
^c Lavrentyev Institute of Hydrodynamics SB RAS, pr. Akad. Lavrentyeva 15, 630090 Novosibirsk

Abstract: Two approaches are proposed for recovering a symmetric $m$-tensor field in a unit disk from the given values of ray transforms. The approaches are based on the method of approximate inverse. The first approach allows us to reconstruct all components of the tensor field, while the second recovers the potentials of the solenoidal part and $m$ potential parts of the tensor field.

Keywords: tensor tomography, method of approximate inverse, adjoint operator, ray transform, Radon transform, tensor field, potential.

UDC: 517.98:519.677

Received: 09.06.2018
Revised: 24.10.2018
Accepted: 15.12.2018

DOI: 10.33048/sibjim.2019.22.110