A Compressive Sampling data gathering approach for Wireless Sensor Networks using a sparse acquisition matrix with abnormal values

Application of Compressive Sampling (CS) to Wireless Sensor Networks (WSNs), is a very promising field. In particular, CS allows to exactly reconstruct a sparse signal using only a few measurements. Hence, it promises to represent a viable solution for reducing data exchange in WSNs, thus prolonging the network lifetime. On the other hand, natural signals are only approximately sparse and, hence, CS entails a reconstruction error, which limits its applicability in many situations. To cope with this impairment, we first consider a CS scheme based on a sparse acquisition matrix, so that only M over N (M ≪ N) randomly chosen nodes in the network send a packet towards the sink. Then, we propose to use a distributed estimation scheme to locally detect whether the data must be forced to transmit or not, thus highly improving the reconstruction quality.