Reconstruction of a phase function of the transport equation

Abstract

In this paper we consider the transport equation used to describe radiation transfer. The phase function is one of its parameter functions. We propose an iterative method for reconstructing it from the observation data. First, we approximate the phase function with a piecewise-linear function. At each iteration step we solve a system of linear equations and find values of the phase function at given nodes. The coefficients of this system can be calculated by the Monte Carlo method. Numerical experiments have been carried out to examine the proposed method.