一种基于QR分解的观测矩阵优化方法  

An optimization method of observation matrix based on QR decomposition

作　　者：周琦宾 吴静[1,2] 余波[1] Zhou Qibin;Wu Jing;Yu Bo(School of Information Engineering,Southwest University of Science and Technology,Mianyang 621000,China;Sichuan Key Laboratory of Special Environmental Robotics,Southwest University of Science and Technology,Mianyang 621000,China)

机构地区：[1]西南科技大学信息工程学院,四川绵阳621000 [2]西南科技大学特殊环境机器人技术四川省重点实验室,四川绵阳621000

出　　处：《电子技术应用》2021年第4期107-111,共5页Application of Electronic Technique

基　　金：特殊环境机器人技术四川省重点实验室基金项目(13ZXTK07)。

摘　　要：在压缩感知理论中,最为关键的问题是观测矩阵的构造。影响图像重建质量的因素包括观测矩阵列向量间的独立性以及观测矩阵与稀疏基间的互相关性。基于此提出了一种优化算法。该算法采用QR分解以增大观测矩阵列独立性,同时对利用等角紧框架(Equiangular Tight Frame,ETF)收缩的Gram矩阵进行优化,通过更新每次梯度下降的方向,加快收敛速度,从而减小观测矩阵与稀疏基间的互相关性。仿真实验结果显示,在信号稀疏度或观测次数相同情况下,该优化观测矩阵的方法在提高图像重建质量与稳定性方面都有一定优势。In compressed sensing theory,the most critical issue is the construction of the observation matrix.The factors that affect the image reconstruction quality include the independence between the observation matrix column vectors and the cross-correlation between the observation matrix and the sparse basis.Based on this,an optimization algorithm is proposed.The algorithm uses QR decomposition to increase the independence of the observation matrix columns,and at the same time optimizes the Gram matrix contracted using an equiangular tight frame(ETF).By updating the direction of each gradient descent,the convergence rate is accelerated to reduce The cross-correlation between the small observation matrix and the sparse basis.Simulation experiment results show that the method of optimizing the observation matrix in this paper has certain advantages in improving the quality and stability of image reconstruction under the same signal sparsity or observation times.

关 键 词：压缩感知 观测矩阵 QR分解 GRAM矩阵 互相关性 

分 类 号：TN912.3[电子电信—通信与信息系统] TP301.6[电子电信—信息与通信工程]