码本在压缩感知矩阵中的应用  

Application of Codebooks in Compressed Sensing Matrixs

作　　者：刘雪梅[1] 史彤 贾丽华 LIU Xue-mei;SHI Tong;JIA Li-hua(College of Science,Civil Aviation University of China,Tianjin 300300,China)

机构地区：[1]中国民航大学理学院,天津300300

出　　处：《数学的实践与认识》2023年第2期216-224,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金青年基金(11701558)。

摘　　要：压缩感知矩阵的构造在压缩感知理论中起着举足轻重的作用.基于线性码和最优码本构造了一类新的压缩感知矩阵,并与DeVore构造的压缩感知矩阵和Gaussian随机矩阵的进比较,从不同的角度分别证明了当参数满足一定的条件时,新构造的压缩感知矩阵具有更好的性能。The construction of compressed sensing matrix plays an important role in compressed sensing theory.In this paper,a new kind of compressed sensing matrix is constructed based on linear code and optimal code book,and compared with DeVore compressed sensing matrix and Gaussian random matrix,it is proved from different angles that the new compressed sensing matrix has better performance when the parameters meet certain conditions.

关 键 词：有限域 仿射空间 码本 Welch界 压缩感知矩阵 

分 类 号：TN911.7[电子电信—通信与信息系统]