Reconstruction of a function and its singular support in a cylinder by tomographic data

In this article we consider problems of reconstruction of a function and its singular support by using tomographic data. The data for the problems are values of the attenuated geodesic x-ray transform which is a set of integrals of an unknown function calculated along geodesics of the Riemannian metric that is used for modelling refraction in a cylinder. The values of the attenuated geodesic x-ray transform are received in a slice-by-slice fan-beam scheme. Our approach is based on the slice-by-slice reconstruction of the sought-for function or its singular support using a modification of well-known operators of back-projection and break indicator.