A new sensor selection scheme for Bayesian learning based sparse signal recovery in WSNs

In this paper, we address the issue of sparse signal recovery in wireless sensor networks (WSNs) based on Bayesian learning. We first formulate a compressed sensing (CS)-based signal recovery problem for the detection of sparse event in WSNs. Then, from the perspective of energy saving and communication overhead reduction of the WSNs, we develop an optimal sensor selection algorithm by employing a lower-bound of the mean square error (MSE) for the MMSE estimator. To tackle the nonconvex difficulty of the optimum sensor selection problem, a convex relaxation is introduced to achieve a suboptimal solution. Both uncorrelated and correlated noises are considered and a low-complexity realization of the sensor selection algorithm is also suggested. Based on the selected subset of sensors, the sparse Bayesian learning (SBL) is utilized to reconstruct the sparse signal. Simulation results illustrate that our proposed approaches lead to a superior performance over the reference methods in comparison.