K-L变换观测矩阵优化算法  

K-L transform optimization algorithm for measurement matrix

作　　者：王海艳 佟岐 连志鹏 汲清波[1] WANG Haiyan;TONG Qi;LIAN Zhipeng;JI Qingbo(College of Information and Communication Engineering,Harbin Engineering University,Harbin 150001,China;Beijing Aerospace Launch Technology Research Institute,Beijing 100076,China)

机构地区：[1]哈尔滨工程大学信息与通信工程学院,哈尔滨150001 [2]北京航天发射技术研究所,北京100076

出　　处：《计算机工程与应用》2018年第19期186-190,215,共6页Computer Engineering and Applications

基　　金：黑龙江省自然科学基金(No.F201407);中央高校基本科研业务费专项资金(No.HEUCFP201769)

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。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 signalto-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.

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 

分 类 号：TN911.73[电子电信—通信与信息系统]