REQUIRED NUMBER OF ITERATIONS FOR SPARSE SIGNAL RECOVERY VIA ORTHOGONAL LEAST SQUARES  

作　　者：Haifeng Li Jing Zhang Jinming Wen Dongfang Li 

机构地区：[1]Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control,College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China [2]College of Information Science and Technology,Jinan University,Guangzhou 510632,China [3]School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China [4]Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074,China

出　　处：《Journal of Computational Mathematics》2023年第1期1-17,共17页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(grant nos.61907014,11871248,11701410,61901160);the Natural Science Foundation of Guangdong province(No.2021A1515010857);Youth Science Foundation of Henan Normal University(grant no.2019QK03);China Postdoctoral Science Foundation(grant no.2019M660557);Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2019).

摘　　要：In countless applications,we need to reconstruct a K-sparse signal x∈R n from noisy measurements y=Φx+v,whereΦ∈R^(m×n)is a sensing matrix and v∈R m is a noise vector.Orthogonal least squares(OLS),which selects at each step the column that results in the most significant decrease in the residual power,is one of the most popular sparse recovery algorithms.In this paper,we investigate the number of iterations required for recovering x with the OLS algorithm.We show that OLS provides a stable reconstruction of all K-sparse signals x in[2.8K]iterations provided thatΦsatisfies the restricted isometry property(RIP).Our result provides a better recovery bound and fewer number of required iterations than those proposed by Foucart in 2013.

关 键 词：Sparse signal recovery Orthogonal least squares(OLS) Restricted isometry property(RIP) 

分 类 号：O17[理学—数学]