一种基于KL-KSVD的测量矩阵优化算法  

The Optimization Design of Measurement Matrix Based on KL-KSVD

作　　者：刘知远 刘有珠[1] 包学才[1] 姜灵 LIU Zhi-yuan;LIU You-zhu;BAO Xue-cai;JIANG Ling(College of Information Engineering,Nanchang Institute of Technology,Nanchang Jiangxi 330099,China)

机构地区：[1]南昌工程学院,江西南昌330099

出　　处：《计算机仿真》2023年第1期388-393,共6页Computer Simulation

基　　金：国家自然科学基金项目(61961026)。

摘　　要：压缩感知可在对数据进行采样的同时完成数据压缩,与传统压缩方法相比能够节省大量时间和存储资源。压缩感知中测量矩阵直接影响信号重建效果,根据减小测量矩阵与稀疏表示矩阵之间的互相关性可优化测量矩阵的原理,提出了一种利用卡洛南-罗伊(Karhunen-Loeve, KL)变换,结合KSVD(K-singular value decomposition)更新稀疏表示矩阵对测量矩阵进行KL-KSVD联合优化的方法。实验结果表明,优化后的测量矩阵比未优化的测量矩阵最终得到的重构图像拥有更高的峰值信噪比,且在压缩比较高的情况下拥有更少的重构时间。Compressed sensing can complete data compression while sensing the data, and compared with traditional compression methods, it can save a lot of time and storage resources. The measurement matrix in compressed sensing directly affects the signal reconstruction effect. According to the principle that the measurement matrix can be optimized by reducing the mutual correlation between the measurement matrix and the sparse representation matrix, an optimization method that uses Karhunen-Loeve transformation joints KSVD to update the sparse representation matrix is proposed to optimize the measurement matrix. The experimental results show that the reconstructed image obtained by the optimized measurement matrix has a higher Peak Signal-to-Noise Ratio(PSNR) than the unoptimized measurement matrix, and has less reconstruction time in the case of high compression.

关 键 词：压缩感知 测量矩阵 互相关性 

分 类 号：TN911.73[电子电信—通信与信息系统]