Compressed Data Separation via ℓ_(q)-Split Analysis with ℓ_(∞)-Constraint  

作　　者：Ming Yang Gu Song Li Jun Hong Lin 

机构地区：[1]School of Mathematical Science,Zhejiang University,Hangzhou,310027,P.R.China [2]Center for Data Science,Zhejiang University,Hangzhou,310027,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第7期1655-1673,共19页数学学报（英文版）

基　　金：Supported by the National Key Research and Development Program of China(Grant No.2021YFA1003500);the NSFC(Grant Nos.U21A20426,11971427,12071426 and 11901518)。

摘　　要：In this paper,we study compressed data separation(CDS)problem,i.e.,sparse data separation from a few linear random measurements.We propose the nonconvex ℓ_(q)-split analysis with ℓ_(∞)-constraint and 0<q≤1.We call the algorithm ℓ_(q)-split-analysis Dantzig selector(ℓ_(q)-split-analysis DS).We show that the two distinct subcomponents that are approximately sparse in terms of two different dictionaries could be stably approximated via the ℓ_(q)-split-analysis DS,provided that the measurement matrix satisfies either a classical D-RIP(Restricted Isometry Property with respect to Dictionaries and ℓ_(2) norm)or a relatively new(D,q)-RIP(RIP with respect to Dictionaries and ℓ_(q)-quasi norm)condition and the two different dictionaries satisfy a mutual coherence condition between them.For the Gaussian random measurements,the measurement number needed for the(D,q)-RIP condition is far less than those needed for the D-RIP condition and the(D,1)-RIP condition when q is small enough.

关 键 词：Data separation ℓ_(q)-split analysis Dantzig selector FRAMES restricted isometry property compressed sensing 

分 类 号：TN911.7[电子电信—通信与信息系统]