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

Abstract

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