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. doi:10.4171/IFB/362. 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.
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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. | ||||||||||||
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Subject Keywords: | Inverse problems, Bayesian level set method, Markov chain Monte Carlo (MCMC) | ||||||||||||
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Issue or Number: | 2 | ||||||||||||
DOI: | 10.4171/IFB/362 | ||||||||||||
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: | 11 Nov 2021 05:11 |
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