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A Bayesian Level Set Method for Geometric Inverse Problems

Iglesias, Marco A. and Lu, Yulong and Stuart, Andrew M. (2016) A Bayesian Level Set Method for Geometric Inverse Problems. Interfaces and Free Boundaries, 18 (2). pp. 181-217. ISSN 1463-9971. https://resolver.caltech.edu/CaltechAUTHORS:20161221-114630868

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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 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:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.4171/IFB/362DOIArticle
http://www.ems-ph.org/journals/show_abstract.php?issn=1463-9963&vol=18&iss=2&rank=3PublisherArticle
https://arxiv.org/abs/1504.00313arXivDiscussion Paper
ORCID:
AuthorORCID
Iglesias, Marco A.0000-0002-8952-717X
Additional Information:© 2016 EMS Publishing House. YL is is supported by EPSRC as part of the MASDOC DTC at the University of Warwick with grant No. EP/HO23364/1. AMS is supported by the (UK) EPSRC Programme Grant EQUIP, and by the (US) Ofice of Naval Research.
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)EP/HO23364/1
Office of Naval Research (ONR)UNSPECIFIED
Subject Keywords:Inverse problems, Bayesian level set method, Markov chain Monte Carlo (MCMC)
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ127
Issue or Number:2
Record Number:CaltechAUTHORS:20161221-114630868
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161221-114630868
Official Citation:Iglesias Marco, Lu Yulong, Stuart Andrew: A Bayesian level set method for geometric inverse problems. Interfaces Free Bound. 18 (2016), 181-217. doi: 10.4171/IFB/362
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73083
Collection:CaltechAUTHORS
Deposited By: Linda Taddeo
Deposited On:21 Dec 2016 20:37
Last Modified:09 Mar 2020 13:18

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