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In this paper, we consider the problem of sparse signal detection based onpartial support set estimation with compressive measurements in a distributednetwork. Multiple nodes in the network are assumed to observe sparse signalswhich share a common but unknown support. While in the traditional compressivesensing (CS) framework, the goal is to recover the complete sparse signal, insparse signal detection, complete signal recovery may not be necessary to makea reliable detection decision. In particular, detection can be performed basedon partially or inaccurately estimated signals which requires lesscomputational burden than that is required for complete signal recovery. Tothat end, we investigate the problem of sparse signal detection based onpartially estimated support set. First, we discuss how to determine the minimumfraction of the support set to be known so that a desired detection performanceis achieved in a centralized setting. Second, we develop two distributedalgorithms for sparse signal detection when the raw compressed observations arenot available at the central fusion center. In these algorithms, the finaldecision statistic is computed based on locally estimated partial support setsvia orthogonal matching pursuit (OMP) at individual nodes. The proposeddistributed algorithms with less communication overhead are shown to providecomparable performance (sometimes better) to the centralized approach when thesize of the estimated partial support set is very small.

Sparse Signal Detection with Compressive Measurements via Partial Support Set Estimation