Clarify Some Issues on the Sparse Bayesian Learning for Sparse Signal Recovery

Sparse Bayesian learning (SBL) is an important family of algorithms for sparse signal recovery and compressed sensing. It has shown superior recovery performance in challenging practical problems, such as highly underdetermined inverse problems, recovering signals with less sparsity, recovering signals based on highly coherent measuring/sensing/dictionary matrices, and recovering signals with rich structure. However, its advantages are smeared in current literature due to some misunderstandings on the parameters of SBL and incorrect parameter settings in algorithm comparison and practical use. This work clarifies some important issues, and serves as a guidance for correctly using SBL.