The least square inversion method for the exterior ray transforms of 3D scalar and vector fields

摘要

> Inversion of the scalar and vector ray transforms is performed in domain R 3 B 3 ( 0 , r 0 ) , ie, with the presence of an obstacle or singularity in the origin. Initially, the ray transforms of the basis functions for the scalar and vector fields are evaluated in an analytical form, and next, the inversion procedure is reduced to a linear system of equations by the use of the least squares method.