Improved RIP-based bounds for guaranteed performance of two compressed sensing algorithms  

作　　者：Yunbin Zhao Zhiquan Luo 

机构地区：[1]Shenzhen Research Institute of Big Data,The Chinese University of Hong Kong,Shenzhen,Shenzhen 518172,China

出　　处：《Science China Mathematics》2023年第5期1123-1140,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.12071307 and 61571384).

摘　　要：Iterative hard thresholding(IHT)and compressive sampling matching pursuit(CoSaMP)are two mainstream compressed sensing algorithms using the hard thresholding operator.The guaranteed performance of the two algorithms for signal recovery was mainly analyzed in terms of the restricted isometry property(RIP)of sensing matrices.At present,the best known bound using the RIP of order 3k for guaranteed performance of IHT(with the unit stepsize)isδ3k<1/√3≈0.5774,and the bound for CoSaMP using the RIP of order 4k isδ4k<0.4782.A fundamental question in this area is whether such theoretical results can be further improved.The purpose of this paper is to affirmatively answer this question and to rigorously show that the abovementioned RIP bound for guaranteed performance of IHT can be significantly improved toδ3k<(√5−1)/2≈0.618,and the bound for CoSaMP can be improved toδ4k<0.5102.

关 键 词：iterative hard thresholding compressive sampling matching pursuit compressed sensing guaranteed performance restricted isometry property 

分 类 号：TN911.7[电子电信—通信与信息系统]