Shrinkage-Based Alternating Projection Algorithm for Efficient Measurement Matrix Construction in Compressive Sensing

Abstract

A simple but efficient measurement matrix construction algorithm (MMCA) within compressive sensing (CS) framework is introduced. In the CS framework, the smaller coherence between the measurement matrix Φ and the sparse matrix (basis) Ψ can lead to better signal reconstruction performance. In this paper, we achieve this purpose by adopting shrinkage and alternating projection technique iteratively. Finally, the coherence among the columns of the optimized measurement matrix Φ and the fixed sparse matrix Ψ can be decreased greatly, even close to the Welch bound. The extensive experiments have been conducted to test the performance of the proposed algorithm, which are compared with that of the state-of-the-art algorithms. We conclude that the recovery performance of greedy algorithms [e.g., orthogonal matching pursuit (OMP) and regularized OMP] using the proposed MMCA outperforms the random algorithm and the algorithms introduced by Elad, Vahid, Hang, and Xu. In addition, the real temperature data gathering and reconstruction in wireless sensor networks have been conducted. The experimental results also show the superiority of MMCA for real temperature data reconstruction comparing with other existing measurement matrix optimization algorithms.