On solving the slice-by-slice three-dimensional 2-tensor tomography problems using the approximate inverse method

Abstract

A numerical solution of the problem of recovering the solenoidal part of a threedimensional symmetric 2-tensor field using the incomplete tomographic data is proposed. The initial data of the problem are values of the ray transform for all straight lines, which are parallel to at least one of the planes from a finite set of planes. We consider two sets of planes, the number of planes in which are three and six. The recovery algorithms are based on the approximate inverse method.