基于Legendre序列的确定性测量矩阵  

Legendre sequence based deterministic measurement matrix

作　　者：崔翔[1] 万洪杰[1] 肖亮[1] 谢晓明[1] CUI Xiang;WAN Hongjie;XIAO Liang;XIE Xiaoming(College of Information Science and Technology, Beijing University of Chemistry Technology, Beijing 100029, China)

机构地区：[1]北京化工大学信息科学与技术学院,北京100029

出　　处：《计算机工程与应用》2016年第16期116-120,共5页Computer Engineering and Applications

摘　　要：近年来,压缩感知理论飞速发展。很多压缩感知的应用中,信号的测量可以通过卷积滤波和之后的二次采样完成。在此基础上,实现了一种由勒让德(Legendre)序列构造的矩阵。该矩阵在经过二次采样之后,得到一种新的确定性测量矩阵。对于一个K-稀疏的信号,通过该测量矩阵可以对信号进行稳定的恢复重建。据仿真结果显示,在对K-稀疏信号进行恢复的过程中,该测量矩阵的恢复效果与高斯随机测量矩阵的应用效果相当。For the past few years, Compressed Sensing(CS)has been developed very fast. In many applications of CS,the data measurement can be achieved by filtering and sub-sampling. In this paper, a new matrix with Legendre Sequenceis constructed, which is based on Convolutional Compressed Sensing. After sub-sampling, a new deterministic measurementmatrix is gotten. For signals that are sparse, the proposed matrix can guarantee a stable recovery. The results show that,the proposed matrix can offer comparable performance with a random Gaussian matrix in K-sparse signal reconstruction.

关 键 词：确定性测量矩阵 卷积压缩感知 相关性 勒让德序列 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]