This article is cited in 13 papers

An Application of the SVD-Method to the Problem of Integral Geometry of 2-Tensor Fields

E. Yu. Derevtsov^ab, A. P. Polyakova<sup>b

a</sup> Novosibirsk State University
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: A problem of integral geometry consisting in determination of a given in unit disk symmetric 2-tensor field by its known ray transforms is considered. Singular value decompositions (SVD) of the operators of longitudinal, transverse and mixed ray transforms that are the integrals of projections of a field at a line of integration are constructed. The results are based essentially on a theorem of a tensor field decomposition and its representation through potentials. The obtained singular value decompositions are constructive and are foundations for the algorithms of a tensor field reconstruction by its known ray transforms.

Keywords: tensor field, integral geometry, tensor tomography, ray transform.

UDC: 517.983:519.642

Received: 18.01.2012

 English version: Journal of Mathematical Sciences, 2014, 202:1, 50–71