Graph spectral compressed sensing for sensor networks

Consider a wireless sensor network with N sensor nodes measuring data which are correlated temporally or spatially. We consider the problem of reconstructing the original data by only transmitting M ≪ N sensor readings while guaranteeing that the reconstruction error is small. Assuming the original signal is “smooth” with respect to the network topology, our approach is to gather measurements from a random subset of nodes and then interpolate with respect to the graph Laplacian eigenbasis, leveraging ideas from compressed sensing. We propose algorithms for both temporally and spatially correlated signals, and the performance of these algorithms is verified using both synthesized data and real world data. Significant savings are made in terms of energy resources, bandwidth, and query latency.

1. INTRODUCTION

For many wireless sensor network (WSN) applications, the signals measured are likely to be correlated either spatially or temporally; i.e., we can find an appropriate transform domain where the signals are compressible. WSNs are characterized by having simple battery-powered wireless nodes with limited energy and communication resources. In order to reduce power consumption and conserve bandwidth (or query latency), it is desirable to apply the philosophy of compressed sensing whereby we directly gather a reduced number of informative measurements rather than gathering a large number of redundant measurements.