加权最小化问题中限制等距性的研究  

Restricted isometry property in the weighted minimization problem

作　　者：张茜雯 王金平 ZHANG Xiwen;WANG Jinping(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2021年第5期39-42,共4页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(62071262).

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.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.

关 键 词：加权限制等距性 加权稀疏 误差估计 加权最小化 

分 类 号：O177.6[理学—数学] O175.5[理学—基础数学]