Sensing, Compression and Recovery for Wireless Sensor Networks: Sparse Signal Modelling

In this paper, we propose a sparsity model that allows the use of Compressive Sensing (CS) for the online recovery of large data sets in real Wireless Sensor Network (WSN) scenarios. We advocate the joint use of CS for the recovery and of Principal Component Analysis (PCA) to capture the spatial and temporal characteristics of real signals. The statistical characteristics of the signals are thus exploited to design the sparsification matrix required by CS recovery. In this paper, we represent this framework through a Bayesian Network (BN) and we use Bayesian analysis to infer and approximate the statistical distribution of the principal components. We show that the Laplacian distribution provides an accurate representation of the statistics of the data measured from real WSN testbeds. Therefore, the joint use of CS and PCA for data recovery in real WSNs is legitimate, and is equivalent to Maximum A Posteriori (MAP) recovery.