Numerical realization of the algorithm of reconstruction of an inhomogeneous medium for an X-ray tomography problem

We study an X-ray tomography problem which is an inverse problem for the differential transport 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; the densities of the output 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 version of numerical realization of the algorithm is presented.