A variational Bayesian method to inverse problems with impulsive noise
Type
ArticleAuthors
Jin, BangtiKAUST Grant Number
KUS-C1-016-04Date
2012-01Permanent link to this record
http://hdl.handle.net/10754/597435
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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.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.Publisher
Elsevier BVJournal
Journal of Computational Physicsae974a485f413a2113503eed53cd6c53
10.1016/j.jcp.2011.09.009