l_(1)-αl_(2)最小化方法基于相干性的稀疏恢复  

l_(1)-αl_(2) Minimization Method for Sparse Recovery Based on Mutual Coherence

作　　者：宋儒瑛[1] 武思琪 关晋瑞 SONG Ru-ying;WU Si-qi;GUAN Jin-rui(School of Mathematics and Statistics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学与统计学院,山西晋中030619

出　　处：《数学的实践与认识》2023年第8期172-179,共8页Mathematics in Practice and Theory

基　　金：山西省应用基础研究计划项目(201901D211423);国家自然科学基金(10221395)。

摘　　要：压缩感知是从一个线性模型y=Ax+e (其中e是一个噪声向量)中稳定或鲁棒恢复一个s-稀疏(或可压缩)信号.l_(1)-αl_(2) (0<α≤1)最小化方法是近几年才出现的一种新的信号恢复的有效方法.文章考虑的是在相干性的框架中通过l_(1)-αl_(2) (0 <α≤1)最小化恢复信号,在l_(2)有界噪声、Dantzig Selector(DS)噪声和脉冲噪声情形下分别给出了保证信号稳定恢复的充分条件.Compressed sensing is stable or robust recovery of an s-sparse(or compressible)signal from a linear model y=Aa+e(where e is a noise vector).l_(1)-αl_(2)2(0<α≤1)minimization method is a new effective method for signal recovery that has emerged in recent years.In this paper,we consider the signal recovery by l_(1)-αl_(2)(0<α≤1)minimization in the framework of mutual coherence,and give sufficient conditions to ensure stable signal recovery under l2 bounded noise,Dantzig Selector(DS)noise and impulse noise,respectively.

关 键 词：压缩感知 信号恢复 l_(1)-αl_(2)最小化 相干性 稀疏恢复 

分 类 号：TN911.7[电子电信—通信与信息系统]