A Bayesian analysis of Compressive Sensing data recovery in Wireless Sensor Networks

In this paper we address the task of accurately reconstructing a distributed signal through the collection of a small number of samples at a data gathering point using compressive sensing (CS) in conjunction with principal component analysis (PCA). Our scheme compresses in a distributed way real world non-stationary signals, recovering them at the data collection point through the online estimation of their spatial/temporal correlation structures. The proposed technique is hereby characterized under the framework of Bayesian estimation, showing under which assumptions it is equivalent to optimal maximum a posteriori (MAP) recovery. As the main contribution of this paper, we proceed with the analysis of data collected by our indoor wireless sensor network (WSN) testbed, proving that these assumptions hold with good accuracy in the considered real world scenarios. This provides empirical evidence of the effectiveness of our approach and proves that CS is a legitimate tool for the recovery of real-world signals in WSNs.