Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in high-dimensional inverse problems using L1-type priors

DOI10.1088/0266-5611/28/12/125012zbMath1266.65013arXiv1206.0262OpenAlexW1990075812MaRDI QIDQ4920045

Felix Lucka

Publication date: 16 May 2013

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.0262

zbMATH Keywords

numerical examplesinverse problemsGibbs samplerBayesian inferenceBayesian inversionvariational regularizationMarkov chain Monte Carlo sampling algorithmsMetropolis-Hastings sampling schemes

Mathematics Subject Classification ID

Related Items (11)

A Proximal Markov Chain Monte Carlo Method for Bayesian Inference in Imaging Inverse Problems: When Langevin Meets Moreau ⋮ Sparse Online Variational Bayesian Regression ⋮ Bayesian approach for inverse interior scattering problems with limited aperture ⋮ Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs ⋮ A hierarchical Bayesian perspective on majorization-minimization for non-convex sparse regression: application to M/EEG source imaging ⋮ Bayesian Inverse Problems with $l_1$ Priors: A Randomize-Then-Optimize Approach ⋮ Optimization-Based Markov Chain Monte Carlo Methods for Nonlinear Hierarchical Statistical Inverse Problems ⋮ Comparison of statistical inversion with iteratively regularized Gauss Newton method for image reconstruction in electrical impedance tomography ⋮ Efficient Bayesian Computation by Proximal Markov Chain Monte Carlo: When Langevin Meets Moreau ⋮ Solution paths of variational regularization methods for inverse problems ⋮ Two Metropolis--Hastings Algorithms for Posterior Measures with Non-Gaussian Priors in Infinite Dimensions

Uses Software

• t-walk
• Rtwalk

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