A Kernel-Based Compressive Sensing Approach for Mobile Data Gathering in Wireless Sensor Network Systems

The recent advances of compressive sensing (CS) have witnessed a great potential of efficient compressive data gathering (CDG) in wireless sensor network systems (WSNSs). However, most existing work on CDG mainly focuses on multihop relaying strategies to improve the performance of data gathering. In this paper, we propose a mobile CDG scheme including a random walk-based algorithm and a kernel-based method for sparsifying sensory data from irregular deployments. The proposed scheme allows a mobile collector to harvest data by sequentially visiting a number of nodes along a random path. More importantly, toward building the gap between CS and machine learning theories, we explore a theoretical foundation for understanding the feasibility of the proposed scheme. We prove that the CS matrices, constructed from the proposed random walk algorithm combined with a kernel-based sparsity basis, satisfy the restricted isometry property. Particularly, we also show that m = O(k log(n/k)) measurements collected by a mobile collector are sufficient to recover a k-sparse signal and t = O(k log(n/k)) steps are required to collect these measurements in a network with n nodes. Finally, we also present extensive numerical results to validate the effectiveness of the proposed scheme by evaluating the performance in terms of energy consumption and the impact of packet losses. The numerical results demonstrate that the proposed scheme is able to not only significantly reduce communication cost but also combat unreliable wireless links under various packet losses compared to the state-of- the-art schemes, which provides an efficient alternative to data relaying approaches for CDG in WSNS.