Leveraging Joint Sparsity in Hierarchical Bayesian Learning

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.