An Introduction to Variational Methods for Graphical Models
Machine Learning
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Stochastic spectral methods for efficient Bayesian solution of inverse problems
Journal of Computational Physics
Journal of Computational Physics
Variational Bayesian inference for a nonlinear forward model
IEEE Transactions on Signal Processing
Hierarchical Bayesian inference for Ill-posed problems via variational method
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Imaging Sciences
An algorithm for the minimization of mixed l1 andl2 norms with application to Bayesian estimation
IEEE Transactions on Signal Processing
Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization
IEEE Transactions on Image Processing
Journal of Computational Physics
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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.