Numerical realization of an algorithm for reconstructing an inhomogeneous medium in an X-ray tomography problem

Under study is the X-ray tomography problem that is an inverse problem for the transport differential equation. We take into account the absorption of particles by the medium and their single scattering. The statement of the problem corresponds to multiple probing. The medium is unknown; while the densities of the outcoming flux averaged over energy are given. The object in question is the discontinuity surfaces of the coefficients of the equation. This corresponds to searching for the boundaries between various substances contained in the medium that we probe. The solution is constructive, and a numerical realization of the obtained algorithm is presented.