A variational Bayesian method to inverse problems with impulsive noise

Bangti Jin

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)423-435
Number of pages13
JournalJournal of Computational Physics
Volume231
Issue number2
DOIs
StatePublished - Jan 2012
Externally publishedYes

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