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The Bayesian formulation of EIT: Analysis and algorithms

Dunlop, Matthew M. and Stuart, Andrew M. (2016) The Bayesian formulation of EIT: Analysis and algorithms. Inverse Problems and Imaging, 10 (4). pp. 1007-1036. ISSN 1930-8345. http://resolver.caltech.edu/CaltechAUTHORS:20170113-072909521

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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:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.3934/ipi.2016030DOIArticle
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=13203PublisherArticle
https://arxiv.org/abs/1508.04106arXivDiscussion Paper
Additional Information:© 2016 American Institute of Mathematical Sciences Received: August 2015; Revised: July 2016; Available Online: October 2016. MMD is supported by EPSRC grant EP/HO23364/1 as part of the MASDOC DTC at the University of Warwick. AMS is supported by EPSRC and ONR. This research utilised Queen Mary's MidPlus computational facilities, supported by QMUL Research-IT and funded by EPSRC grant EP/K000128/1.
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)EP/HO23364/1
Office of Naval Research (ONR)UNSPECIFIED
QMUL Research-ITUNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)EP/K000128/1
Subject Keywords:Inverse problems, ill-posed problems, electrical impedance tomography, Bayesian regularisation, geometric priors, level set methodology
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ126
Classification Code:2010 Mathematics Subject Classification. Primary: 62G05, 65N21; Secondary: 92C55.
Record Number:CaltechAUTHORS:20170113-072909521
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170113-072909521
Official Citation:The Bayesian formulation of EIT: Analysis and algorithms Pages : 1007 - 1036 Matthew M. Dunlop and Andrew M. Stuart
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73479
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:18 Jan 2017 19:16
Last Modified:01 Aug 2017 22:51

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