亚高斯随机矩阵的稀疏恢复  

Sparse recovery of sub-Gaussian random matrix

作　　者：宋儒瑛[1] 郑珂 关晋瑞[1] Song Ruying;Zheng Ke;Guan Jinrui(Department of mathematics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学系,山西晋中030619

出　　处：《纯粹数学与应用数学》2022年第4期520-532,共13页Pure and Applied Mathematics

基　　金：山西省应用基础研究计划项目(201901D211423);山西省高等学校科技创新项目(2019L0783)。

摘　　要：对于一般的压缩感知模型,当模型中系数矩阵的每一项都是亚高斯随机变量并且稀疏矩阵满足限制等距性质时,在测量值满足最优条件m≥csln(e N/s)的情况下,模型的s稀疏解也可以通过?1最小化得到.文章中首先借助概率分布范数给出了三个重要的辅助定理,最后给出主要结论的证明并且通过一个简单的实验验证了最后的定理.For the general compressed sensing model,when each term of the coefficient matrix in the model is a sub Gaussian random variable and the sparse matrix satisfies the limited isometric property,the s sparse solution of the model can also be obtained by?1-minimization when the measured value meets the optimal condition m≥csln(e N/s).In this paper,three important auxiliary theorems are given with the help of probability distribution norm.Finally,the proof of the main conclusions is given,and the final theorem is verified by a simple experiment.

关 键 词：压缩感知 稀疏恢复 ?1最小化 亚高斯随机变量 随机矩阵 

分 类 号：O178[理学—数学]