关键词: 压缩感知, 观测矩阵, Karhunen-Loeve（K-L）变换, 协方差矩阵, 互相关性

Abstract: The research of measurement matrix is very important in compressed sensing, and the optimization of measurement matrix is one of the key problems in the study of measurement matrix. Based on the idea of reducing the mutual correlation between measurement matrix and sparse matrix to optimize the measurement matrix, an optimization algorithm of K-L transform measurement matrix is proposed. The algorithm transforms the sensing matrix by using the eigenvector matrix of the original signal covariance matrix, thus, the mutual correlation between measurement matrix and sparse matrix is reduced, then the optimized measurement matrix is obtained. Simulation results show that the peak signal-to-noise ratio of the reconstructed image by optimized measurement matrix is greater than the peak signal-to-noise ratio of the reconstructed image by not optimized measurement matrix. Especially in the case of a small number of observations, the reconstructed image with the optimized measurement matrix has high precision.

Key words: Compressed Sensing（CS）, measurement matrix, Karhunen-Loeve（K-L） transform, covariance matrix, mutual correlation