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A Bayesian level set method for geometric inverse problems
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Iglesias, Marco, Lu, Yulong and Stuart, A. M. (2016) A Bayesian level set method for geometric inverse problems. Interfaces and Free Boundaries, 18 (2). pp. 181-217. doi:10.4171/IFB/362 ISSN 1463-9963.
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Official URL: http://dx.doi.org/10.4171/IFB/362
Abstract
We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the object of the inference. Whilst the level set methodology has been widely used for the solution of geometric inverse problems, the Bayesian formulation that we develop here contains two significant advances: firstly it leads to a well-posed inverse problem in which the posterior distribution is Lipschitz with respect to the observed data, and may be used to not only estimate interface locations, but quantify uncertainty in them; and secondly it leads to computationally expedient algorithms in which the level set itself is updated implicitly via the MCMC methodology applied to the level set function – no explicit velocity field is required for the level set interface. Applications are numerous and include medical imaging, modelling of subsurface formations and the inverse source problem; our theory is illustrated with computational results involving the last two applications.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Inverse problems (Differential equations), Bayesian statistical decision theory | ||||||
| Journal or Publication Title: | Interfaces and Free Boundaries | ||||||
| Publisher: | European Mathematical Society Publishing House | ||||||
| ISSN: | 1463-9963 | ||||||
| Official Date: | 19 September 2016 | ||||||
| Dates: |
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| Volume: | 18 | ||||||
| Number: | 2 | ||||||
| Page Range: | pp. 181-217 | ||||||
| DOI: | 10.4171/IFB/362 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 3 March 2017 | ||||||
| Date of first compliant Open Access: | 8 March 2017 | ||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), United States. Office of Naval Research | ||||||
| Grant number: | EP/HO23364/1, Programme Grant EQUIP (EPSRC) |
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