Deterministic Measurement Matrix Generation for Compressive Data Gathering and Reconstruction in WSNs

Abstract

In this paper, a novel deterministic measurement matrix construction algorithm (DMMCA) within compressive sensing (CS) framework was introduced for gathering and reconstructing the compressive data in large scale of wireless sensor networks (WSNs). Random measurement matrix (e.g., Gaussian matrix) has been widely used because it presents small coherence with almost any sparse basis. However, decreasing the coherence between the measurement matrix and the fixed sparse basis will improve the CS performance greatly. We achieve this purpose by adopting shrinking and Singular Value Decomposition (SVD) technique iteratively. In addition, we conducted several experiments to measure the performance of the proposed algorithm and compare it with the existing algorithms. The recovery performance of greedy algorithms (e.g., orthogonal matching pursuit) with the proposed measurement matrix construction method outperforms the traditional random, Elad's, Abolghasemi's and Xu's algorithms. Finally, the practical experimental results in WSNs present the same positive results as the simulations.