Distributed Compressive Sensing Reconstruction via Common Support Discovery

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 our method is using the Fr´ echet 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. The superior reconstruction quality of the proposed method is demonstrated by both computer-generated signals and real data gathered by a WSN located in the Intel Berkeley Research lab.