Forward and Inverse Problem Formulation of Optical Tomography Based on Equation of Radiative Transfer
Raheel Muzzammel *
Department of Electrical Engineering, University of Lahore, Lahore, Pakistan
Muhammad Sarwar Ehsan
Department of Computer Engineering, University of Central Punjab, Lahore, Pakistan
*Author to whom correspondence should be addressed.
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.
Keywords: Optical Tomography, equation of radiative transfer, regularized least square, discrete ordinate method, finite volume method, adjoint method