噪声情形下块稀疏信号恢复的充分条件  

Sufficient conditions for recovering block sparse noisy signals

作　　者：单浠 王金平 SHAN Xi;WANG Jinping(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2024年第3期44-49,共6页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(62071262).

摘　　要：压缩感知是一种有效的信号采集技术,利用信号的可压缩性,通过采样与非线性算法完美地恢复信号.基于压缩感知理论,本文通过块正交匹配追踪算法,研究在l_(∞)有界噪声影响下恢复块稀疏信号和强衰减块稀疏信号的约束等距性质,给出保证该算法准确恢复原信号的充分条件,并通过数值实验对影响稀疏信号性能的因素进行分析比较.Compressed sensing uses the compressibility of signals to entirely recover signals by sampling techniques and nonlinear algorithms,hence regarded as an effective signal acquisition technology.Based on the theory of compressed sensing,taking the l_(∞) bounded noise as the example,we study the RIP properties in recovering block sparse signals and the strongly-decaying block sparse signals by the BOMP algorithm,and we provide necessary sufficient conditions to ensure recovering the signals.Finally,we analyze and compare the factors which affect the performance of sparse signals by means of numerical experiments.

关 键 词：BOMP算法 l_(∞)有界噪声 稀疏信号 强衰减块稀疏信号 

分 类 号：O177.6[理学—数学] O175.5[理学—基础数学]