The semi-analytical method for inversion of a weighted vector ray transform in three dimensions

Abstract

An inversion of the weighted vector ray transform is performed jointly with the inversion of the scalar ray transform for the weighted function [Formula: see text]. Initially, the ray transform of the basis vector functions for the vector field [Formula: see text] is evaluated in an analytical form and then the inversion problem is reduced by the method of the least squares to a linear system of equations.