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This paper presents a novel signal reconstruction method based on the Distributed Compressive Sensing (DCS) framework for application to Wireless Sensor Networks (WSN). The proposed method exploits both the intra-sensor correlation and the inter-sensor correlation to reduce the number of samples required for recovering the original signals. An innovative feature of the authors' method is using the Frechet mean of the signals to discover the common support of their sparse representations in some basis. Then a new greedy algorithm, called Precognition Matching Pursuit (PMP), is proposed to further reduce the number of required samples with the knowledge of the common support.
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