ORACLE INEQUALITIES FOR CORRUPTED COMPRESSED SENSING  

作　　者：Liping Yin Peng Li 

机构地区：[1]School of Mathematics and Statistics,Lanzhou University,Lanzhou 730000,China

出　　处：《Journal of Computational Mathematics》2025年第2期461-492,共32页计算数学(英文)

基　　金：supported by the Natural Science Foundation of China(Grant No.12201268);by the Science and Technology Program of Gansu Province of China(Grant No.21JR7RA511).

摘　　要：In this paper,we establish the oracle inequalities of highly corrupted linear observationsb=Ax_(0)+f_(0)+e∈R^(m).Here the vectorx_(0)∈R^(m)is a(approximately)sparse signal and∈R^(n)n>>mis a sparse error vector with nonzero entries that can be possible infinitely large,erepresents the Gaussian random noise vector.We extend the oracle inequality■for Dantzig selector and Lasso models in[E.J.Candès and T.Tao,Ann.Statist.,35(2007),2313-2351]and[T.T.Cai,L.Wang,and G.Xu,IEEE Trans.Inf.Theory,56(2010),3516-3522]to■for the extended Dantzig selector and Lasso models.Here{|λf_(0)(j)|^(2),σ^(2)}is the solution of the extended model,and■is the balance parameter between■.

关 键 词：Corrupted compressed sensing Oracle inequality Extended Dantzig selector Extended Lasso Generalized restricted isometry property 

分 类 号：O17[理学—数学]