Sparse Signal Detection with Compressive Measurements via Partial Support Set Estimation

Abstract: In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which share a common but unknown support. While in the traditional compressive sensing (CS) framework, the goal is to recover the complete sparse signal, in sparse signal detection, complete signal recovery may not be necessary to make a reliable detection decision. In particular, detection can be performed based on partially or inaccurately estimated signals which requires less computational burden than that is required for complete signal recovery. To that end, we investigate the problem of sparse signal detection based on partially estimated support set. First, we discuss how to determine the minimum fraction of the support set to be known so that a desired detection performance is achieved in a centralized setting. Second, we develop two distributed algorithms for sparse signal detection when the raw compressed observations are not available at the central fusion center. In these algorithms, the final decision statistic is computed based on locally estimated partial support sets via orthogonal matching pursuit (OMP) at individual nodes. The proposed distributed algorithms with less communication overhead are shown to provide comparable performance (sometimes better) to the centralized approach when the size of the estimated partial support set is very small.