Stepwise solution to an inverse problem for the radiative transfer equation as applied to tomography

An X-ray tomography problem is formulated and analyzed within the framework of a mathematical model based on the polychromatic stationary radiative transfer equation with no collision integral. It is assumed that the outgoing radiation density is only given, and the task is to find the surface of an internal inclusion on whose boundary the coefficients of the equation may have jump discontinuities. The uniqueness of the solution is proved, and the corresponding solution algorithm is outlined. A feature of this work is that the research technique is local in character. This makes it possible to use only some of the available data, and the procedure can be stopped at an intermediate stage of the reconstruction, which can be useful in applications.