The Bayesian formulation of EIT: Analysis and algorithms

Matthew M.  Dunlop; Andrew M.  Stuart

doi:10.3934/ipi.2016030

Article Contents

2016, Volume 10, Issue 4: 1007-1036. Doi: 10.3934/ipi.2016030

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The Bayesian formulation of EIT: Analysis and algorithms

Matthew M. Dunlop^1, and
Andrew M. Stuart^1,

1.
Computing & Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125

Received: July 31, 2015

Revised: June 30, 2016

Published: October 2016

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Abstract

We provide a rigorous Bayesian formulation of the EIT problem in an infinite dimensional setting, leading to well-posedness in the Hellinger metric with respect to the data. We focus particularly on the reconstruction of binary fields where the interface between different media is the primary unknown. We consider three different prior models -- log-Gaussian, star-shaped and level set. Numerical simulations based on the implementation of MCMC are performed, illustrating the advantages and disadvantages of each type of prior in the reconstruction, in the case where the true conductivity is a binary field, and exhibiting the properties of the resulting posterior distribution.

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Mathematics Subject Classification: Primary: 62G05, 65N21; Secondary: 92C55.

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