Complex multitask Bayesian compressive sensing

An effective complex multitask Bayesian compressive sensing (CMT-BCS) algorithm is proposed to recover sparse or group sparse complex signals. The existing multitask Bayesian compressive sensing (MT-CS) algorithm is powerful in recovering multiple real-valued sparse solutions. However, a large class of sensing problems deal with complex values. A simple approach, which decomposes a complex value into independent real and imaginary components, does not take into account the group sparsity of these two components and thus yields poor recovery performance. In this paper, we first introduce the CMT-BCS algorithm that jointly treats the real and imaginary components, and then derive a fast and accurate algorithm for the estimation of the prior parameters by solving a surrogate convex function. The proposed CMT-BCS algorithm achieves effective complex sparse signal recovery and outperforms MT-CS and complex group Lasso.