A variational Bayesian method to inverse problems with impulsive noise

• Published in: Journal of computational physics Vol. 231; no. 2; pp. 423 - 435
• Main Author: Jin, Bangti
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 2012; Elsevier
• Subjects: Algorithms; Bayesian analysis; Computational techniques; Exact sciences and technology; Heat transfer; Impulsive noise; Inverse problems; Mathematical methods in physics; Mathematical models; Noise; Numerical analysis; Physics; Robust Bayesian; Robustness; Variational method; Impulsive noise; Variational method; Inverse problems; Robust Bayesian; Variational methods; Numerical method; Nonlinear problems; Calculation methods; Divergences; Algorithms; Problem solving; Models; Calculation; Bayes methods; Flux transfer; Heat transfer; Thermal conduction
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2011.09.009

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.