Reconstruction in the cone-beam vector tomography with two sources

Abstract

In this paper, we consider the inverse problem for the cone beam transform of vector fields. This transform maps a vector field to its line integrals along rays coming out from points on a given source trajectory. We proved that the solenoidal part of the field can be reconstructed, if the trajectory satisfies the Kirillov–Tuy condition of order 2. It means that every plane, intersecting the support of the field, intersects the trajectory twice. An exact inversion formula is presented. A reconstruction algorithm, based on the obtained formula is developed. Numerical experiments confirm reliability of the algorithm.