A variational Bayesian method to inverse problems with impulsive noise

Jin, Bangti

A variational Bayesian method to inverse problems with impulsive noise

Type

Article

Authors

Jin, Bangti

KAUST Grant Number

KUS-C1-016-04

Date

2012-01

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.

Acknowledgements

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.