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Methods for the Inverse Problem in Optical Tomography

  • S. R. Arridge

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.

Keywords

optical tomography Green’s functions Born approximation Rytov approximation finite element method optimisation 

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • S. R. Arridge
    • 1
  1. 1.Dept. Computer ScienceUniversity College LondonLondonUK

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