Numerical solution of a problem of refractive tomography in a tube domain

A problem of refractive tomography is considered for a tube domain with a given arbitrary varying absorption and refraction of a special type modelled by means of a Riemannian metric. We propose a numerical solution of the problem based on the consecutive solution of a series of two-dimensional problems. We show that such an approach is possible if the domain has a sufficiently large family of totally geodesic submanifolds of dimension two. Riemannian metrics admitting the existence of the set are contructed. We propose an algorithm for an approximate solution of the problem based on the least squares method.