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The Bayesian formulation of EIT : analysis and algorithms

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Stuart, A. M. and Dunlop, Matthew M. (2016) The Bayesian formulation of EIT : analysis and algorithms. Inverse Problems and Imaging, 10 (4). pp. 1007-1036. doi:10.3934/ipi.2016030

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Official URL: http://dx.doi.org/10.3934/ipi.2016030

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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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
R Medicine > RC Internal medicine
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Electrical impedance tomography -- Mathematical models, Bayesian statistical decision theory
Journal or Publication Title: Inverse Problems and Imaging
Publisher: American Institute of Mathematical Sciences
ISSN: 1930-8337
Official Date: November 2016
Dates:
DateEvent
November 2016Published
31 October 2016Available
9 September 2016Accepted
August 2015Submitted
Date of first compliant deposit: 3 March 2017
Volume: 10
Number: 4
Page Range: pp. 1007-1036
DOI: 10.3934/ipi.2016030
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Engineering and Physical Sciences Research Council (EPSRC), Great Britain. Office for Nuclear Regulation (ONR)
Grant number: EP/HO23364/1, EP/K000128/1 (EPSRC)
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