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    A variational Bayesian method to inverse problems with impulsive noise

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    Type
    Article
    Authors
    Jin, Bangti
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2012-01
    Permanent link to this record
    http://hdl.handle.net/10754/597435
    
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    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.
    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 BV
    Journal
    Journal of Computational Physics
    DOI
    10.1016/j.jcp.2011.09.009
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jcp.2011.09.009
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