Leveraging Joint Sparsity in Hierarchical Bayesian Learning

SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 442-472, June 2024.
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 hyperparameters 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 multicoil magnetic resonance imaging application, demonstrate that our new approach consistently outperforms commonly used hierarchical Bayesian methods.