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A General Framework for Iterative Reconstruction Algorithms in Optical Tomography, Using a Finite Element Method
 Simon R. Arridge,
 Martin Schweiger
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Abstract
In this paper we present several schemes for solving the inverse problem in Optical Tomography. We first set the context of Optical Tomography and discuss alternative photon transport models and measurement schemes. We develop the inverse problem as the optimisation of an objective functions and develop three classes of algorithms fors its solution: Newton methods, linearised methods, and gradient methods. We concentrate on the use numerical methods based on Finite Elements, and discuss how efficient methods may be developed using adjoint solutions. A taxonomy of algorithms is given, with an analysis of their spatial and temporal complexity.
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 Title
 A General Framework for Iterative Reconstruction Algorithms in Optical Tomography, Using a Finite Element Method
 Book Title
 Computational Radiology and Imaging
 Book Subtitle
 Therapy and Diagnostics
 Pages
 pp 4570
 Copyright
 1999
 DOI
 10.1007/9781461215509_4
 Print ISBN
 9781461271895
 Online ISBN
 9781461215509
 Series Title
 The IMA Volumes in Mathematics and its Applications
 Series Volume
 110
 Series ISSN
 09406573
 Publisher
 Springer New York
 Copyright Holder
 SpringerVerlag New York, Inc.
 Additional Links
 Topics
 Keywords

 Optical Tomography
 Diffusion
 Inverse Problems
 Finite Elements
 eBook Packages
 Editors

 Christoph Börgers ^{(2)}
 Frank Natterer ^{(3)}
 Editor Affiliations

 2. Department of Mathematics, Tufts University
 3. Institut für Numerische und instrumentelle Mathematik, Universität Münster
 Authors

 Simon R. Arridge ^{(4)}
 Martin Schweiger ^{(5)}
 Author Affiliations

 4. Department of Computer Science, University College London, WC1E 6BT, UK
 5. Department of Medical Physics, University College London, WC1E 6JA, UK
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