Leveraging joint sparsity in hierarchical Bayesian learning
This provides an incremental improvement for researchers and practitioners working with sparse signal recovery in applications like medical imaging.
The authors tackled the problem of inferring jointly sparse parameter vectors from multiple measurement vectors by developing a hierarchical Bayesian learning approach with joint-sparsity-promoting priors. Their method consistently outperformed existing hierarchical Bayesian methods in numerical experiments, including a multi-coil MRI application.
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.