加权最小化问题中限制等距性的研究 (Restricted isometry property in the weighted minimization problem)

ZHANG Xiwen; WANG Jinping

加权最小化问题中限制等距性的研究

张茜雯,王金平.加权最小化问题中限制等距性的研究[J].宁波大学学报(理工版),2021,34(5):39-42.DOI:

ZHANG Xiwen,WANG Jinping.Restricted isometry property in the weighted minimization problem[J].Journal of Ningbo University(Natural Science & Engineering Edition),2021,34(5):39-42.DOI:

《宁波大学学报（理工版）》 [ISSN:1001-5132/CN:33-1134/N] 年: 2021 卷: 34 期: 5 栏目: 数学研究页码: 39-42 出版日期: 2021-09-10

Title:	Restricted isometry property in the weighted minimization problem
作者:	张茜雯, 王金平
Author(s):	ZHANG Xiwen, WANG Jinping
关键词:	加权限制等距性; 加权稀疏; 误差估计; 加权最小化
Keywords:	weighted restricted isometry property; weighted sparsity; error estimation; weighted minimization
分类号:	O177.6; O175.5
文献标识码:	A
摘要:	本文针对加权最小化问题, 首先给出了测量矩阵的加权限制等距性(RIP)与加权鲁棒零空间特性(rNSP)的定义, 证明了加权RIP蕴含着加权rNSP. 最后以加权RIP作为充分条件, 给出了解重构的误差估计.
Abstract:	In this paper, the focus is set on the weighted minimization case. The definitions are first proposed of the weighted restricted isometry property (RIP) and the weighted robust null space property (rNSP) of measurement matrix. Then the assumption that the weighted RIP implies the weighted rNSP is proven. Finally, the reconstruction of error estimations based on the weighted RIP is derived as a sufficient condition.
参考文献 /References:	[1] Foucart S, Lai M J. Sparsest solutions of under- determined linear systems via lq minimization for 0[j].>[2] Rauhut H, Ward R. Interpolation via weighted l1 minimization[J]. Applied and Computational Harmonic Analysis, 2016, 40:321-351. [3] Huo H Y, Sun W C, Xiao L. New conditions on stable recovery of weighted sparse signals via weighted l1 minimization[J]. Circuits, Systems, and Signal Processing, 2018, 37:2866-2883. [4] Wang Y, Wang J J, Xu Z B. On recovery of block-sparse signals via mixed l2/lq (0[5] Gao Y, Peng J G, Yue S G. Stability and robustness of the l2/lq-minimization for block sparse recovery[J]. Signal Processing, 2017, 137:287-297. [6] Aldroubi A, Chen X, Powell A. Stability and robustness of lq minimization using null space property[C]//The 9th International Conference on Sampling Theory and Applications, 2011. [7] Chartrand R, Staneva V. Restricted isometry properties and nonconvex compressive sensing[J]. Inverse Problems, 2008, 24:035020. [8] Baraniuk R, Davenport M, DeVore R et al. A simple proof of the restricted isometry property for random matrices[J]. Constructive Approximation, 2008, 28:253-263.
备注/Memo:	收稿日期: 2020－11－28. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（62071262）. 第一作者: 张茜雯（1997－）, 女, 河南焦作人, 在读硕士研究生, 主要研究方向: 积分变换与图像处理. E-mail: 875252582@qq.com *通信作者: 王金平（1962－）, 男, 湖北武汉人, 博士/教授, 主要研究方向: 积分变换与图像处理. E-mail: wangjinping@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/

加权最小化问题中限制等距性的研究

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