A Bayesian level set method for geometric inverse problems
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...
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| Format: | Article |
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European Mathematical Society
2016
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| Online Access: | https://eprints.nottingham.ac.uk/40925/ |
| _version_ | 1848796164274520064 |
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| author | Iglesias, Marco Lu, Yulong Stuart, Andrew |
| author_facet | Iglesias, Marco Lu, Yulong Stuart, Andrew |
| author_sort | Iglesias, Marco |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:43:38Z |
| format | Article |
| id | nottingham-40925 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:38Z |
| publishDate | 2016 |
| publisher | European Mathematical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-409252020-05-04T20:02:43Z https://eprints.nottingham.ac.uk/40925/ A Bayesian level set method for geometric inverse problems Iglesias, Marco Lu, Yulong Stuart, Andrew 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. European Mathematical Society 2016-05 Article PeerReviewed Iglesias, Marco, Lu, Yulong and Stuart, Andrew (2016) A Bayesian level set method for geometric inverse problems. Interfaces and Free Boundaries, 18 (2). pp. 181-217. ISSN 1463-9971 Inverse problems Bayesian level set method Markov chain Monte Carlo (MCMC) http://www.ems-ph.org/journals/show_abstract.php?issn=1463-9963&vol=18&iss=2&rank=3 doi:10.4171/IFB/362 doi:10.4171/IFB/362 |
| spellingShingle | Inverse problems Bayesian level set method Markov chain Monte Carlo (MCMC) Iglesias, Marco Lu, Yulong Stuart, Andrew A Bayesian level set method for geometric inverse problems |
| title | A Bayesian level set method for geometric inverse problems |
| title_full | A Bayesian level set method for geometric inverse problems |
| title_fullStr | A Bayesian level set method for geometric inverse problems |
| title_full_unstemmed | A Bayesian level set method for geometric inverse problems |
| title_short | A Bayesian level set method for geometric inverse problems |
| title_sort | bayesian level set method for geometric inverse problems |
| topic | Inverse problems Bayesian level set method Markov chain Monte Carlo (MCMC) |
| url | https://eprints.nottingham.ac.uk/40925/ https://eprints.nottingham.ac.uk/40925/ https://eprints.nottingham.ac.uk/40925/ |