基于l_(p)有界噪声的压缩数据分离  

Compressed Data Separation under l_(p)Bounded Noise

作　　者：李玲玉 黄尉[1] Ling Yu LI;Wei HUANG(School of Mathematics,Hefei University of Technology,Hefei 230009,P.R.China)

机构地区：[1]合肥工业大学数学学院,合肥230009

出　　处：《数学学报（中文版）》2023年第3期527-538,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(91538112)。

摘　　要：本文考虑l_(p)有界噪声约束下的压缩数据分离问题,即从压缩测量数据中重建信号的不同稀疏子成分.为了重构不同框架D_(1)∈R^(n×d_(1))和D_(2)∈R^(n×d_(2))下(近似)稀疏的不同子成分,我们首先提出了l_(1)-αl_(2)分解分析算法,在测量矩阵满足一定的约束等距性条件且字典之间满足某个相互相干性条件时,此算法可以处理不同噪声干扰下的信号分离问题.此外,基于经典Dantzig Selector模型,我们还引入了l_(1)-αl_(2)分解分析Dantzig Selector算法,在适当条件下此算法也可以稳定分离压缩数据.数值实验表明,l_(1)-αl_(2)最小化算法对于冗余紧框架下的数据分离问题具有鲁棒性和稳定性.We consider the compressed data separation problem under ep bounded noise,that is,to reconstruct different sparse subcomponents of signals from compressed measurements.In order to reconstruct different subcomponents that are(approximate)sparse in terms of diferent frames D_(1)∈R^(n×d_(1))and D_(2)∈R^(n×d_(2)),we first propose the l_(1)-αl_(2)split analysis algorithm,which can deal with the problem of signal separation under the corruption of different kinds of noises,when thc measurement matrix meets a certain restricted isometry property and the dictionaries meet a certain mutual coherence condition.In addition,based on the classical Dantzig Selector,we also introduce l_(1)-αl_(2)split analysis Dantzig Selector.It can also stably separate compressed data under appropriate conditions.Numerical experiments are carried out to show that l_(1)-αl_(2)minimization are robust and stable for the separation of compressed data with redundant tight frames.

关 键 词：压缩数据分离 l_(1)-αl_(2)最小化 l_(p)有界噪声 限制等距性条件 紧框架 

分 类 号：O177.2[理学—数学]