A numerical solver based on B-splines for 2D vector field tomography in a refracting medium

Efficient and stable numerical solvers for vector tomography problems taking refractions into account are subject of current research. This article is concerned with the problem of reconstructing a 2D-vector field in a refracting medium from its known longitudinal or transverse ray transform. The refraction is modeled using a Riemannian metric in the domain under consideration. We propose a numerical solver that is based on the least squares method where we use a finite basis consisting of B-splines as basis functions. In that sense the method can be seen as a projection method for minimizing an L2-data fitting term. Numerical simulations show a good performance of that method, also compared to methods relying on exact inversion formulas.