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

摘要： 观测矩阵的研究在压缩感知中尤为重要，其中观测矩阵的优化是观测矩阵研究中的关键问题之一。根据减小观测矩阵与稀疏矩阵之间的互相关性达到优化观测矩阵的思想，提出了K-L变换观测矩阵优化算法。该算法利用原始信号协方差矩阵的特征向量矩阵对传感矩阵进行变换，从而减小观测矩阵与稀疏矩阵之间的互相关性，进而得到优化后的观测矩阵。仿真结果表明，优化后的观测矩阵重构图像的峰值信噪比值大于未优化观测矩阵重构图像的峰值信噪比值，尤其是在观测数目较少的情况下，用该算法优化后的观测矩阵重构的图像具有较高的精度。

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