Summary: Chapter 1
METHODS FOR THE INVERSE PROBLEM
IN OPTICAL TOMOGRAPHY
Simon R. Arridge
Dept. Computer Science, University College London
Gower Street, London, UK
S.Arridge@cs.ucl.ac.uk
Abstract In this paper we give a brief overview of the image reconstruction prob­
lem 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 ap­
proximations 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
minimise a least­squares error functional. We introduce the Finite Ele­
ment 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 ap­

Source: Arridge, Simon - Department of Computer Science, University College London

Collections: Computer Technologies and Information Sciences