An efficient data gathering and reconstruction method in WSNs based on compressive sensing

In this paper, we introduce a very simple deterministic measurement matrix design algorithm(SDMMDA), based on which the data gathering and reconstruction in wireless sensor networks(WSNs) are greatly enhanced. Although SDM-MDA is very simple, but the measurement and reconstruction performance is more efficient than the random matrix and the matrix designed by schnass. The basic principle of the proposed algorithm can be stated as follows. First, generating a random redundant matrix Φ. Second, constructing a Gram matrix G, which can be denoted as Φ^T * Φ. Third, decreasing the absolute value of the off-line entries of the Gram matrix. Finally, mutual coherence of the random measurement matrix can be decreased greatly and the compressive data gathering as well as the signal reconstruction performance are greatly improved simultaneously. Besides that, we adopt backtracking-based adaptive OMP(BAOMP) method to reconstruct the original signal gathered by WSNs. By using BAOMP,We need not to know the signal sparse level K anymore. Extensive simulations and practical experiments of WSNs have shown that reconstruction performance of the compressive data gathered with CS method is improved greatly by using the proposed SDMMDA and BAOMP.