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Title: Expectation propagation for nonlinear inverse problems – with an application to electrical impedance tomography

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of efficiently delivering reliable estimates of the posterior mean and covariance, thereby providing an inverse solution together with quantified uncertainties. Some theoretical properties of the iterative algorithm are discussed, and the efficient implementation for an important class of problems of projection type is described. The method is illustrated with one typical nonlinear inverse problem, electrical impedance tomography with complete electrode model, under sparsity constraints. Numerical results for real experimental data are presented, and compared with that by Markov chain Monte Carlo. The results indicate that the method is accurate and computationally very efficient.
Authors:
 [1] ;  [2]
  1. Center for Industrial Mathematics, University of Bremen, Bremen D-28344 (Germany)
  2. Department of Mathematics, University of California, Riverside, University Ave. 900, Riverside, CA 92521 (United States)
Publication Date:
OSTI Identifier:
22230871
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 259; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; APPROXIMATIONS; ELECTRODES; IMPEDANCE; ITERATIVE METHODS; MARKOV PROCESS; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; NONLINEAR PROBLEMS; TOMOGRAPHY