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

Journal Article · Sat Feb 15 04:00:00 EST 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2013.12.010· OSTI ID:22230871

Gehre, Matthias ^[1]; Jin, Bangti ^[2]

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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)

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.

• OSTI ID: 22230871
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 259; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALGORITHMS
APPROXIMATIONS
ELECTRODES
IMPEDANCE
ITERATIVE METHODS
MARKOV PROCESS
MATHEMATICAL SOLUTIONS
MONTE CARLO METHOD
NONLINEAR PROBLEMS
TOMOGRAPHY