基于滤波的压缩感知信号采集方案  

Filter-based signal collection scheme in compressed sensing

作　　者：王天荆[1,2] 郑宝玉[2] 杨震[2] 

机构地区：[1]南京工业大学理学院,南京210009 [2]南京邮电大学宽带无线通信与传感网技术教育部重点实验室,南京210003

出　　处：《仪器仪表学报》2013年第3期573-581,共9页Chinese Journal of Scientific Instrument

基　　金：国家重大基础研究973计划(2011CB302903);国家自然科学基金(60971129);江苏省自然科学基金(BK2011793);中国博士后科学基金(20100481167);江苏省博士后科学基金(1101022B)资助项目

摘　　要：压缩感知中常选择随机矩阵作为测量矩阵来进行随机线性投影采样,但过多自由元素使得随机矩阵硬件实现、存储和计算困难,因此设计易于硬件实现的测量矩阵是将压缩感知推向实用化的关键。根据信号通过有限脉冲响应滤波器的差分方程,提出一种新的基于滤波的压缩感知信号采集方案,实现了信号在托普利兹测量矩阵下有用信息的高效获取。仿真实验说明托普利兹测量矩阵比随机矩阵更易实现信号采样和重构,并具有硬件实现简单、存储量小、计算复杂度低的优点。The random matrices are usually used as the measurement matrices to perform random linear projection sampling in compressed sensing, but too many free elements bring difficulty to the hardware realization, storage and calculation of the random matrices. Therefore, designing the measurement matrices that are easy to be realized with hardware is the key of the practicality of compressed sensing. According to the difference equation that describes the behavior of signal passing through Finite Impulse Response （FIR） filter, a novel filter-based signal collection scheme in compressed sensing is proposed to effectively acquire the useful information of the signal with the Toeplitz measurement matrices. Simulation results demonstrate that compared with the random matrices, the Toeplitz measurement matrices can implement the signal collection and reconstruction better, and have the advantages of simple hardware realization,less storage requirement and low computational complexity.

关 键 词：压缩感知 测量矩阵 托普利兹矩阵 有限等距特性 

分 类 号：TN912.3[电子电信—通信与信息系统] TH73[电子电信—信息与通信工程]