Measurement matrix construction algorithm for sparse signal recovery

Abstract

A simple measurement matrix construction algorithm (MMCA) within compressive sensing framework is introduced. In compressive sensing, the smaller coherence between the measurement matrix and the sparse dictionary (basis) can have better signal reconstruction performance. Random measurement matrices (e.g., Gaussian matrix) have been widely used because they present small coherence with almost any sparse base. However, optimizing the measurement matrix by decreasing the coherence with the fixed sparse base will improve the CS performance greatly, and the conclusion has been well proved by many prior researchers. Based on above analysis, we achieve this purpose by adopting shrinking and Singular Value Decomposition (SVD) technique iteratively. Finally, the coherence among the columns of the optimized matrix and the sparse dictionary can be decreased greatly, even close to the welch bound. In addition, we established several experiments to test the performance of the proposed algorithm and compare with the state of art algorithms. We conclude that the recovery performance of greedy algorithms (e.g., orthogonal matching pursuit) by using the proposed measurement matrix construction method outperforms the traditional random matrix algorithm, Elad's algorithm, Vahid's algorithm and optimized matrix algorithm introduced by Xu.