A Bayesian Analysis of Compressive Sensing Data Recovery in Wireless Sensor Networks.pdfVIP

A Bayesian Analysis of Compressive Sensing Data Recovery in Wireless Sensor Networks Riccardo Masiero, Giorgio Quer, Michele Rossi and Michele Zorzi Department of Information Engineering, University of Padova via Gradenigo 6/B – 35131, Padova, Italy Email: {riccardo.masiero, giorgio.quer, rossi, zorzi}@dei.unipd.it Abstract—In this paper we address the task of accurately re- signals through the online estimation of their statistics. The constructing a distributed signal through the collection of a small effectiveness of our approach for data gathering and recovery number of samples at a data gathering point using Compressive has been proved in [5] for both synthetic and real signals. Sensing (CS) in conjunction with Principal Component Analysis (PCA). Our scheme compresses in a distributed way real world In this paper we investigate the statistical distribution of non-stationary signals, recovering them at the data collection the principal components of signals gathered from an actual point through the online estimation of their spatial/temporal Wireless Sensor Network (WSN) deployment. This analysis correlation structures. The proposed technique is hereby char- provides an explanation of the good results that we have acterized under the framework of Bayesian estimation, showing obtained in [5] and proves that CS is a legitimate tool under which assumptions it is equivalent to optimal maximum a posteriori (MAP) recovery. As the main contribution of this for the recovery of real-world signals in WSNs. The main paper, we proceed with the analysis of data collected by our