Linear Prediction for data compression and recovery enhancement in Wireless Sensors Networks

Compressed Sensing (CS) has been successfully applied within Wireless Sensors Networks (WSN). We consider the problem of data recovery from a subset of few sensor readings collection at a fusion center in the case of spatially correlated large WSN. We exploit the data spatial correlation to derive a sparse representation of the signal and consider 1-D reading of the WSN. To this end, we propose a novel approach based on Linear Prediction Coding (LPC) as a sparsifying transform. Then, the Orthogonal Matching Pursuit (OMP) CS algorithm is used for original data recovery. We adopt a uniform spatial correlation model which induces a problem with an unknown degree of sparsity. In this scenario, the OMP operates with a stopping rule conditioned by the residual observation norm. Our approach outperforms other 1-D conventional sparsity-inducing methods such as DCT, PCA and DFT across a wide range of spatial correlation levels. The obtained enhancement is especially obtained for low number of measurements, thus leading to a significant power consumption reduction.