Energy-efficient collection of sparse data in wireless sensor networks using sparse random matrices

We consider the energy efficiency of collecting sparse data in wireless sensor networks using compressive sensing (CS). We use a sparse random matrix as the sensing matrix, which we call Sparse Random Sampling (SRS). In SRS, only a randomly selected subset of nodes, called the source nodes, are required to report data to the sink. Given the source nodes, we intend to construct a data gathering tree such that (1) it is rooted at the sink and spans every source node and (2) the minimum residual energy of the tree nodes after the data collection is maximized.We first show that this problem is NP-complete and then develop a polynomial time algorithm to approximately solve the problem.We greedily construct a sequence of data gathering trees over multiple rounds and propose a polynomial-time algorithm to collect linearly combined measurements at each round. We show that the proposed algorithm is provably near-optimal. Simulation and experimental results show that the proposed algorithm excels not only in increasing the minimum residual energy, but also in extending the network lifetime.