A numerical inversion of the ray transform operator in refraction tomography

We suggest an approach to an approximate inversion of the ray transform operator acting on functions given in Riemannian domain. We construct an inversion algorithm with usage of ray and beam transforms, back-projection operator and Fourier transform. The algorithm is investigated by numerical experiments. The results of simulation are compared with results of the other algorithm constructed on the base of least square method by means of $B$-splines.