Compressive Data Aggregation from Poisson point process observations

This paper introduces Stochastic Compressive Data Aggregation (S-CDA) for wireless sensor networks (WSN) under random deployments. The Poisson point process (PPP) models the random deployment, and at the same time, allows the efficient implementation of an adequate sparsifying matrix, the random discrete Fourier transform (RDFT). The signal recovery is based on the RDFT which reveals the frequency content of smooth signals, such as temperature or humidity maps, which consist of few frequency components. The recovery methods are based on the accelerated iterative hard thresholding (AIHT) which sets all but the largest (in magnitude) frequency components to zero. The adoption of the PPP allows to analyze the communication and compression aspects of S-CDA using previous results from stochastic geometry and compressed sensing, respectively.