Bayesian learning for the Type-3 joint sparse signal recovery

Compressed sensing (CS) is a signal acquisition paradigm that utilises the finding that a small number of linear projections of a sparse signal have enough information for stable recovery. This paper develops a Bayesian CS algorithm to simultaneously recover multiple signals that follow the Type-3 joint sparse model, where signals share a non-sparse common component and have distinct sparse innovation components. By employing the expectation-maximization (EM) algorithm, the proposed algorithm iteratively updates the estimates of the common component and innovation components. In particular, we find that the update rule for the non-sparse common component in the proposed algorithm, differs from all the other methods in the literature, and we provides an interpretation that gives a valuable insight into why the proposed algorithm is successful in estimating the non-sparse common component. The superior performance of the proposed algorithm is demonstrated by numerical simulation results.This work is supported by EPSRC Research Grant EP/K033700/1; the Natural Science Foundation of China (61401018, U1334202); the Fundamental Research Funds for the Central Universities (No. 2014JBM14 9); the State Key Laboratory of Rail Traffic Control and Safety (RCS2016ZT014) of Beijing Jiaotong University.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by IEEE