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International Journal for Uncertainty Quantification

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.v1.i1.10
pages 1-17

MARGINALIZATION OF UNINTERESTING DISTRIBUTED PARAMETERS IN INVERSE PROBLEMS—APPLICATION TO DIFFUSE OPTICAL TOMOGRAPHY

Ville Kolehmainen
University of Eastern Finland, Department of Applied Physics, P.O.B. 1627, FI-70211 Kuopio, Finland
Tanja Tarvainen
Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland
Simon R. Arridge
Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK
Jari P. Kaipio
Department of Mathematics, University of Auckland, New Zealand; and Department of Physics and Mathematics, University of Eastern Finland

ABSTRACT

With inverse problems there are often several unknown distributed parameters of which only one may be of interest. Since assigning incorrect fixed values to the uninteresting parameters usually leads to a severely erroneous model, one is forced to estimate all distributed parameters simultaneously. This may increase the computational complexity of the problem significantly. In the Bayesian framework, all unknowns are generally treated as random variables and estimated simultaneously and all uncertainties can be modeled systematically. Recently, the approximation error approach has been proposed for handling uncertainty and model-reduction-related errors in the models. In this approach approximate marginalization of these errors is carried out before the estimation of the interesting variables. In this paper we discuss the adaptation of the approximation error approach to the marginalization of uninteresting distributed parameters. As an example, we consider the marginalization of scattering coefficient in diffuse optical tomography.