基于伪随机序列的压缩感知测量矩阵构造  

Construction of compressed sensing measurement matrix based on pseudo random sequence

作　　者：杨俊坡 刘文远 YANG Jun-po;LIU Wen-yuan(School of Electronic Information and Artificial Intelligence, Shaanxi University of Science & Technology, Xi′an 710021, China)

机构地区：[1]陕西科技大学电子信息与人工智能学院,陕西西安710021

出　　处：《陕西科技大学学报》2021年第4期161-165,共5页Journal of Shaanxi University of Science & Technology

基　　金：陕西省科技厅自然科学基础研究计划项目(2020JQ732);陕西科技大学博士科研启动基金项目(126021886,2018BJ-01)。

摘　　要：针对压缩感知理论中确定性测量矩阵的构造问题,基于二进制伪随机序列,提出具有采样和重构性能的确定性测量矩阵.利用有限域、编码理论和伪随机序列等理论,引入奇数和偶数情况的低相关性二进制伪随机序列,在此基础上,提出了适用于压缩感知算法的确定性测量矩阵.理论分析和软件仿真实验表明,在同样的信号输入条件下,与高斯随机矩阵和伯努利随机矩阵相比,基于伪随机序列的测量矩阵具有更加优秀的信号重构性能和更低的实现难度.Aiming at the construction of deterministic measurement matrix in compressed sensing theory,a deterministic measurement matrix with sampling and reconstruction performance is proposed based on binary pseudo-random sequence.Based on the finite field theory,coding theory and pseudo-random sequence theory,low correlation binary pseudo-random sequences in odd and even cases are introduced respectively.On this basis,a deterministic measurement matrix suitable for compressed sensing algorithm is proposed.Theoretical analysis and software simulation experiments show that under the same signal input conditions,compared with Gaussian random matrix and Bernoulli random matrix,the measurement matrix based on pseudo-random sequence has better signal reconstruction performance and lower implementation difficulty.

关 键 词：有限域 压缩感知 迹函数 伪随机序列 测量矩阵 

分 类 号：TN911.72[电子电信—通信与信息系统]