Optimized Measurement Matrix for Compressive Sensing

The recently developed theory of compressive sensing (CS) is a new framework for simultaneous signal sampling and compression. Its goal is to minimize the number of samples that need to be taken for faithful reconstruction. The samples are typically drawn by using some random projection measurement matrix. In this paper, we study the optimization of the CS random measurement matrices. Starting with an initial random matrix, the proposed method could simply reduce the average mutual coherence of the original CS measurement matrix to get a better-performance sampling matrix. The experimental results on 1-D sparse signal and 2-D compressible signal demonstrate that the proposed method leads to better CS reconstruction performance with low extra computational cost.