Singular value decomposition of a normal Radon transform operator acting on 3D symmetric 2-tensor fields

Abstract

A problem of 3D 2-tensor field potential part reconstruction by the known value of its normal Radon transform is considered. A singular value decomposition of the operator is constructed for solving the problem. Basic fields are constructed with the use of Jacobi polynomials, Gegenbauer polynomials, and spherical harmonics.