第一作者宋欢欢女，硕士生，1989年4月生

通信作者叶庆卫男，副教授，1970年4月生

基于稀疏AR建模信号去噪研究与应用

宋欢欢，叶庆卫，王晓东，周宇

(宁波大学信息科学与工程学院， 浙江宁波315211)

摘要：为去掉在不同环境、设备下所采集信号中的不同分布形态噪声，引入稀疏优化求解思路构建新的去噪算法。设信号的AR模型系数是稀疏的，且噪声对AR模型系数影响均衡分布，则可用采集的含噪声信号构建稀疏AR模型有效消除噪声。用含噪声信号构建AR系数矩阵作为过完备稀疏基，通过多次重复随机抽取方式获得多个欠定方程组；利用稀疏优化求解算法获取AR模型稀疏系数；据稀疏系数平均值重构信号。仿真实验表明，信号含噪声较大时该算法较经典小波及中值滤波去噪效果更好。

关键词：多频信号；AR模型；稀疏表示；过完备稀疏基

收稿日期：2013-10-21修改稿收到日期：2014-04-03

中图分类号:TP391.4文献标志码：A

基金项目：国家科技支撑计划项目(2011BAF14B04);江苏省自然科学基金资助项目(BK2011504);江苏高校优势学科建设工程资助项目(PAPD);江苏省博士后基金资助项目(1201024B);国家博士后基金(2012M521008)

A new algorithm of signal de-noising based on sparse AR model

SONGHuan-huan,YEQing-wei,WANGXiao-dong,ZHOUYu(Information Science and Engineering College, Ningbo University, Ningbo 315211, China)

Abstract:A actual signal always contains noise due to different surroundings and collecting devices. And the noise has different forms. A signal de-noise algorithm is an important pre-processing tool. Here, a new de-noise algorithm was proposed based on sparse optimization. It was assumed that coefficients of signal’s AR model are sparse and the noise effect on coefficients of AR model has an even distribution. A sparse AR model was built for the signal with noise. The AR coefficient matrix was constructed with the noised signal, and the matrix was taken as the over-completed sparse basis. Several underdetermined equation sets were obtained by extracting randomly some rows several times from the over-completed sparse basis. Then, the sparse AR coefficients were solved with the sparse optimization algorithm. At last, the AR coefficients were averaged, and the de-noised signal was reconstructed with the averaged AR coefficients. The simulation results showed that the de-noising effect obtained with the proposed algorithm is better than those of the classical wavelet de-noising algorithm and the median filtering de-noising algorithm.

Key words:multi-frequency signal; AR model; sparse representation; over-completed sparse base

在实际实验中信号分析只能针对采集的信号进行研究。由于外界环境、检测设备不完善造成所采信号含噪声干扰，有用信息被噪声淹没，无法对信号准确分析研究，故须先对信号进行去噪预处理。小波去噪为常用的多频信号去噪方法。基于小波变换的信号去噪算法有诸多阈值方法，如文献[2]对阈值方法缺陷进行阐述：在信号不连续区域会出现Gibbs现象；……