一种基于拟牛顿法的CS投影矩阵优化算法  

An Optimization Method for CS Projection Matrix Based on Quasi-Newton Method

作　　者：郑红[1] 李振[1] 黄盈[1] 

机构地区：[1]北京航空航天大学自动化科学与电气工程学院,北京100191

出　　处：《电子学报》2014年第10期1977-1982,共6页Acta Electronica Sinica

基　　金：国家自然科学基金(No.60543006);教育部博士点基金(No.201003259)

摘　　要：压缩感知(Compressed Sensing,CS)理论中,投影矩阵优化是一类通过提高观测数据信息量而改善性能的方法.由于投影矩阵与稀疏字典内积构造的Gram矩阵必定奇异,基于广义逆矩阵求解方法存在计算精度的问题.本文提出了一种利用拟牛顿法的CS投影矩阵优化算法.该算法分为两步:一是利用阈值函数约束Gram矩阵非对角线元素,使投影矩阵与稀疏字典的互相关系数逼近Welch界;二是采用秩2校正得到Hessian阵逆近似去修正梯度搜索方向.两个步骤交替执行,直到解出符合优化要求的投影矩阵.该算法始终保持下降性,具有超线性收敛速度,避免了矩阵函数二阶导数复杂的计算,计算量较小.实验结果表明,当信号稀疏度或观测数据相同时,本文算法的重构结果优于其他算法.In compressed sensing（ CS for short） theory,the projection matrix optimization is a kind of approach of improving performance by increasing the amount of information of observational data.This paper presents a CS projection matrix optimization algorithm based on quasi-New ton method.The algorithm is divided into tw o steps.First,use threshold function to restrain the non-diagonal elements in order to make the M utual Coherence betw een the projection matrix and sparse dictionary approximate Welch bound.Second,use Rank tw o to check and get Hessian matrix inverse to amend the direction of the gradient search.Tw o steps are alternately performed until the projection matrix w hich meets the requirement of the optimal solution is w orked out.This algorithm alw ays maintains descent and has a super-linear convergence rate,w hich requires less computation.Experimental results show that w hen signal sparse degree or observation data is identical,this proposed algorithm outperforms other algorithms.

关 键 词：压缩感知 投影矩阵优化 GRAM矩阵 拟牛顿法 

分 类 号：TN911.7[电子电信—通信与信息系统]