Simultaneous Sparse Bayesian Learning With Partially Shared Supports

TL;DR: This letter provides a Bayesian approach that extends the sparse Bayesian learning for such a joint-sparse model where sparse vectors just have partially shared supports, and an efficient deterministic Bayesian inference algorithm is developed.

Abstract: Many simultaneous sparse estimation approaches focus on joint estimation of multiple sparse vectors with a common support from given linear observations, which is however too strict in some real applications. In this letter, instead of forcing a common support, a general joint-sparse model is considered where sparse vectors just have partially shared supports. This letter provides a Bayesian approach that extends the sparse Bayesian learning for such a joint-sparse model. The proposed Bayesian framework is composed of a number of parametric models that correspond to distinct patterns of partially shared supports, and an efficient deterministic Bayesian inference algorithm is developed. The proposed method is characterized as a tuning parameter-free approach, which can effectively infer the underlying sparse structure and also the noise level. Experimental results show the superiority of the proposed approach.