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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
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 | ||||||||||
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| Subjects: | Q Science > QA Mathematics R Medicine > RC Internal medicine |
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| 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: |
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| 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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