STABLE RECOVERY OF SPARSE SIGNALS WITH NON-CONVEX WEIGHTED r-NORM MINUS 1-NORM  

作　　者：Jianwen Huang Feng Zhang Xinling Liu Jianjun Wang Jinping Jia Runke Wang 

机构地区：[1]School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China [2]School of Mathematics and Statistics,Tianshui Normal University,Tianshui 741001,China [3]chool of Mathematics and Statistics,Southwest University,Chongqing 400715,China [4]Key Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan Province,School of Mathematics and Information,China West Normal University,Nanchong 637009,China [5]School of Mathematics and Statistics,Southwest University,Chongqing 400715,China [6]School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China [7]College of Resources and Environmental Engineering,Tianshui Normal University,Tianshui 741001,China

出　　处：《Journal of Computational Mathematics》2025年第1期43-62,共20页计算数学(英文)

基　　金：supported in part by the National Natural Science Foundation of China(Grant Nos.12101454,12101512,12071380,62063031);by the Chongqing Normal University Foundation Project(Grant No.23XLB013);by the Fuxi Scientific Research Innovation Team of Tianshui Normal University(Grant No.FXD2020-03);by the National Natural Science Foundation of China(Grant No.12301594);by the China Postdoctoral Science Foundation(Grant No.2021M692681);by the Natural Science Foundation of Chongqing,China(Grant No.cstc2021jcyj-bshX0155);by the Fundamental Research Funds for the Central Universities(Grant No.SWU120078);by the Natural Science Foundation of Gansu Province(Grant No.21JR1RE292);by the College Teachers Innovation Foundation of Gansu Province(Grant No.2023B-132);by the Joint Funds of the Natural Science Innovation-driven development of Chongqing(Grant No.2023NSCQ-LZX0218);by the Chongqing Talent Project(Grant No.cstc2021ycjh-bgzxm0015).

摘　　要：Given the measurement matrix A and the observation signal y,the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system y=Ax+z,where x is the s-sparse signal to be recovered and z is the noise vector.Zhou and Yu[Front.Appl.Math.Stat.,5(2019),Article 14]recently proposed a novel non-convex weighted l_(r)-l_(2)minimization method for effective sparse recovery.In this paper,under newly coherence-based conditions,we study the non-convex weighted l_(r)-l_(2)minimization in reconstructing sparse signals that are contaminated by different noises.Concretely,the results reveal that if the coherenceμof measurement matrix A fulfillsμ<k(s;r,α,N),s>1,α^(1/r)N(1/2)<1,then any s-sparse signals in the noisy scenarios could be ensured to be reconstructed robustly by solving weighted l_(r)-l_(2)minimization non-convex optimization problem.Furthermore,some central remarks are presented to clear that the reconstruction assurance is much weaker than the existing ones.To the best of our knowledge,this is the first mutual coherence-based sufficient condition for such approach.

关 键 词：Compressed sensing Sparse recovery Mutual coherence Sufficient condition 

分 类 号：O17[理学—数学]