Distributed Data Aggregation for Sparse Recovery in Wireless Sensor Networks

We consider the approximate sparse recovery problem in multi-hop Wireless Sensor Networks (WSNs) using Compressed Sensing/Compressive Sampling (CS). The goal is to recover the n-dimensional data values by querying only m ≪ n sensors based on some linear projection of sensor readings. To solve this problem, a distributed compressive sparse sampling (DCSS) algorithm is proposed based on sparse binary CS measurement matrix. Each sensor first samples the environment independently, then the fusion center (FC), acting as a pseudo-sensor, samples the sensor network to select a subset of sensors (m out of n) that respond to the FC through shortest path for data recovery purpose. The sparse binary matrix is designed using the unbalanced expander graph which achieves the state-of-the-art performance for CS schemes. This binary matrix can be interpreted as a sensor selection matrix whose fairness is analyzed. Extensive experiments on both synthetic and real data sets show that by querying only the minimum amount of m sensors using the DCSS algorithm, the CS recovery accuracy outperforms existing sparse random matrices and can be as good as those using random dense measurement matrices but using much less number of sensors. We also show that the sparse binary measurement matrix works well on compressible data which has the closest recovery result to the known best k-term approximation. The recovery is robust against noisy measurements and does not require regular WSN deployments (e.g., grids). The sparsity and binary properties of the measurement matrix contribute, to a great extent, the reduction of the in-network communication cost as well as the computational burden.