修正FR谱共轭梯度法在信号恢复问题中的应用  

Application of Modified FR Conjugate Gradient Method in Signal Recovery

作　　者：晁丽佳 张永富[1] CHAO Lijia;ZHANG Yongfu(College of Mathematics and Physics,Inner Mongolia University for Nationalities,Tongliao Inner Mongolia 028000,China)

机构地区：[1]内蒙古民族大学数理学院,内蒙古通辽028000

出　　处：《重庆师范大学学报（自然科学版）》2023年第5期11-18,共8页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.11961053);内蒙古民族大学博士科研启动基金项目(No.BS424);内蒙古民族大学科学技术研究项目(No.NMDYB17154)。

摘　　要：基于压缩感知理论,为解决稀疏信号恢复问题,在经典的FR共轭梯度法分析的基础上,给出一种基于谱梯度方法的修正FR谱共轭梯度法,该方法结合了FR、DY、CD等6种经典共轭梯度法的共轭参数部分特点。另外,证明了所给方法在Wolfe线搜索下具有下降方向且全局收敛,通过与其他2种算法的数值结果比较显示,本文算法具有一定优势。同时,信号重构结果表明,提出的方法重构信噪比高,耗时少,能有效的应用于稀疏信号的恢复问题。Based on compressive sensing theory,it aims to solve the problem of sparse signal recovery.On the basis of the analysis of the classical FR conjugate gradient method,a modified FR spectral conjugate gradient method based on the spectral gradient method is proposed.This method combines some characteristics of conjugate parameters of six classical conjugate gradient methods,such as FR,DY,and CD.Additionally,it is proved that the given method has a descending direction and global convergence under the Wolfe line search.Comparing with the numerical results of the other two algorithms,it is shown that the given optimization algorithm has some advantages.The signal reconstruction results show that the proposed method has high signal-to-noise ratio and less time-consuming,and can be effectively applied to the recovery of sparse signals.

关 键 词：信号恢复 谱共轭梯度法 全局收敛性 WOLFE线搜索 

分 类 号：O224[理学—运筹学与控制论]