A variational Bayesian method to inverse problems with impulsive noise

Handle URI:
http://hdl.handle.net/10754/597435
Title:
A variational Bayesian method to inverse problems with impulsive noise
Authors:
Jin, Bangti
Abstract:
We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback-Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm. © 2011 Elsevier Inc.
Citation:
Jin B (2012) A variational Bayesian method to inverse problems with impulsive noise. Journal of Computational Physics 231: 423–435. Available: http://dx.doi.org/10.1016/j.jcp.2011.09.009.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Jan-2012
DOI:
10.1016/j.jcp.2011.09.009
Type:
Article
ISSN:
0021-9991
Sponsors:
This work is supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The author is grateful to two anonymous referees for their constructive comments, which have led to an improved presentation of the manuscript.
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Full metadata record

DC FieldValue Language
dc.contributor.authorJin, Bangtien
dc.date.accessioned2016-02-25T12:33:11Zen
dc.date.available2016-02-25T12:33:11Zen
dc.date.issued2012-01en
dc.identifier.citationJin B (2012) A variational Bayesian method to inverse problems with impulsive noise. Journal of Computational Physics 231: 423–435. Available: http://dx.doi.org/10.1016/j.jcp.2011.09.009.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2011.09.009en
dc.identifier.urihttp://hdl.handle.net/10754/597435en
dc.description.abstractWe propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback-Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm. © 2011 Elsevier Inc.en
dc.description.sponsorshipThis work is supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The author is grateful to two anonymous referees for their constructive comments, which have led to an improved presentation of the manuscript.en
dc.publisherElsevier BVen
dc.subjectImpulsive noiseen
dc.subjectInverse problemsen
dc.subjectRobust Bayesianen
dc.subjectVariational methoden
dc.titleA variational Bayesian method to inverse problems with impulsive noiseen
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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