Leveraging joint sparsity in hierarchical Bayesian learning

Abstract

We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed hyper-parameters to enforce joint sparsity. The resulting joint-sparsity-promoting priors are combined with existing Bayesian inference methods to generate a new family of algorithms. Our numerical experiments, which include a multi-coil magnetic resonance imaging application, demonstrate that our new approach consistently outperforms commonly used hierarchical Bayesian methods.

30 pages, 15 figures

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Cited by in corpus (2)

• Bayesian decomposition using Besov priors
• Generalized sparsity-promoting solvers for Bayesian inverse problems: Versatile sparsifying transforms and unknown noise variances