Sensing, Compression, and Recovery for WSNs: Sparse Signal Modeling and Monitoring Framework

We address the problem of compressing large and distributed signals monitored by a Wireless Sensor Network (WSN) and recovering them through the collection of a small number of samples. We propose a sparsity model that allows the use of Compressive Sensing (CS) for the online recovery of large data sets in real WSN scenarios, exploiting Principal Component Analysis (PCA) to capture the spatial and temporal characteristics of real signals. Bayesian analysis is utilized to approximate the statistical distribution of the principal components and to show that the Laplacian distribution provides an accurate representation of the statistics of real data. This combined CS and PCA technique is subsequently integrated into a novel framework, namely, SCoRe1: Sensing, Compression and Recovery through ON-line Estimation for WSNs. SCoRe1 is able to effectively self-adapt to unpredictable changes in the signal statistics thanks to a feedback control loop that estimates, in real time, the signal reconstruction error. We also propose an extensive validation of the framework used in conjunction with CS as well as with standard interpolation techniques, testing its performance for real world signals. The results in this paper have the merit of shedding new light on the performance limits of CS when used as a recovery tool in WSNs.