基于压缩感知的伪随机等效采样信号重构  

Pseudo-random Equivalent Sampling Signal Reconstruction Based on Compressed Sensing

作　　者：李家强[1,2] 董石明 陈金立[1,2] 朱艳萍[2] 陈焱博 LI Jiaqiang;DONG Shiming;CHEN Jinli;ZHU Yanping;CHEN Yanbo(Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters,Nanjing University of Information Science and Technology,Nanjing 210044,China;School of Electronic and Information Engineering,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学气象灾害预报预警与评估协同创新中心,南京210044 [2]南京信息工程大学电子与信息工程学院,南京210044

出　　处：《电讯技术》2019年第10期1127-1131,共5页Telecommunication Engineering

基　　金：国家自然科学基金资助项目(61801231)

摘　　要：伪随机等效采样利用采样周期数与采样点数间的互质关系使各采样点均匀复现于同一周期,从而达到较高的等效采样速率。然而为了精确重构出原始信号,需大量采样数据,因此导致采样时间过长,实时性能差。针对上述问题,提出了一种基于压缩感知理论的伪随机等效采样信号重构方法,通过构造伪随机等效采样观测矩阵并选择离散傅里叶变换基建立稀疏重构模型,然后利用压缩感知中的正交匹配追踪算法求解该模型,从而重构出原始信号。仿真实验表明,所提方法在采样点个数40时,重构成功率达99.73%。Pseudo-random equivalent sampling method,which utilizes the co-prime relationship between the number of sampling periods and the number of sampling points,achieves a higher equivalent sampling rate with uniformly reproduced sampling point in the same period.However,a large amount of sampling data is needed to be reconstruct accurately the original signal,so the sampling time is too long and the real-time performance is poor.For above problems,a compressed sensing based pseudo-random equivalent sampling signal reconstruction method is proposed.Through constructing a pseudo-random equivalent sampling observation matrix,the discrete Fourier transform basis is selected to establish a sparse reconstruction model.Then the orthogonal matching pursuit(OMP)algorithm is applied to solve the model and reconstruct the original signal.Simulation results demonstrate that,when the number of sampling points is 40,the success rate of reconstruction achieves 99.73%.

关 键 词：伪随机等效采样 压缩感知 观测矩阵 正交匹配追踪算法 

分 类 号：TN911.7[电子电信—通信与信息系统]