Forward and Inverse Problem Formulation of Optical Tomography Based on Equation of Radiative Transfer

Abstract

Optical tomography is non-invasive diagnostic technique. Mathematically, it is related to the evaluation of optical parameters from the equation of radiative transfer with diffused boundary measurements. Since the radiative transfer equation in expressed in the form of phase space, it is quite challenging to solve it computationally. In this paper, reconstruction is based on equation of radiative transfer in frequency domain and termination criteria for forward problem is proposed as ratio of residues. Directional and spatial variables of equation of radiative transfer are discretized with discrete ordinate method and finite volume method respectively. The sparse structure of matrices of complex valued algebraic equations is formulated.