Methods for the Inverse Problem in Optical Tomography

Abstract

In this paper we give a brief overview of the image reconstruction problem in Optical Tomography together with some examples of simulation reconstructions using a numerical optimisation scheme. We discuss first a Diffraction Tomography approach, wherein it is assumed that the measurement is of a scattered wave representing the difference in fields between an unknown and a known state. Both the Born and Rytov approximations are presented and lead to a linear reconstruction problem. Secondly we discuss image reconstruction as an Optimization problem, wherein we develop a model capable of predicting the total field and minimize a least-squares error functional. We introduce the Finite Element Method as a tool for calculating photon density fields in general complex geometries. By means of this method we simulate a number of images and their reconstructions using both a Born and Rytov approximation. The Rytov approximation appears superior in all cases.