Abstract
In this work, we develop a novel robust Bayesian approach to inverse problems with data errors following a skew-t distribution. A hierarchical Bayesian model is developed in the inverse problem setup. The Bayesian approach contains a natural mechanism for regularization in the form of a prior distribution, and a LASSO type prior distribution is used to strongly induce sparseness. We propose a variational type algorithm by minimizing the Kullback-Leibler divergence between the true posterior distribution and a separable approximation. The proposed method is illustrated on several two-dimensional linear and nonlinear inverse problems, e.g. Cauchy problem and permeability estimation problem.
Original language | English (US) |
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Pages (from-to) | 377-393 |
Number of pages | 17 |
Journal | Journal of Computational Physics |
Volume | 301 |
DOIs | |
State | Published - Nov 15 2015 |
Bibliographical note
Publisher Copyright:© 2015 Elsevier Inc.
Keywords
- Bayesian inverse problems
- Hierarchical Bayesian model
- Kullback-Leibler divergence
- Variational approximation
ASJC Scopus subject areas
- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics