Multivariated Bayesian Compressive Sensing in Wireless Sensor Networks

Recently, compressive sensing has been studied in wireless sensor networks, which allows an aggregator to recover the desired sparse signal with fewer active sensor nodes. In this paper, we consider heterogeneous sensing environments, where the sensing quality varies due to the differences in the physical environment of each sensor node. We consider a Bayesian compressive sensing approach and propose two efficient algorithms that decrease the number of active sensor nodes while maintaining high performance. Both the selection algorithms aim to reduce the estimation error by minimizing the determinant of the error covariance matrix, which is proportional to the volume of the confidence ellipsoid. The first algorithm is the centralized greedy selection algorithm, which can achieve a nearly optimal solution in terms of the minimum confidence ellipsoid. It can also achieve almost the same level of performance as the combinatorial selection method, but has a lower complexity and outperforms the conventional convex relaxation method. The second algorithm is the decentralized selection algorithm, which is derived by approximating the determinant of the error covariance matrix. Unlike the centralized greedy algorithm, it can be done by each sensor node without heavy overhead or high complexity. Furthermore, we prove that the decentralized selection algorithm becomes equivalent to the centralized greedy algorithm as the number of sensor nodes increases. Our simulation results show that the centralized greedy selection algorithm provides the best performance while the decentralized algorithm performs nearly as well as the centralized algorithm as the number of sensor nodes increases.