COMPLEX MULTITASK BAYESIAN COMPRESSIVE SENSING

An effective complex multitask Bayesian compressive sens-ing (CMT-BCS) algorithm is proposed to recover sparse or group sparse complex signals. The existing multitask Bayesian compressive sensing (MT-CS) algorithm is power-ful in recovering multiple real-valued sparse solutions. How-ever, 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 com-ponents 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. Index Terms — Compressive sensing, Bayesian infer-ence, multitask learning, multiple measurement vecto