基于稀疏AR建模信号去噪研究与应用  

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

作　　者：宋欢欢[1] 叶庆卫[1] 王晓东[1] 周宇[1] 

机构地区：[1]宁波大学信息科学与工程学院,浙江宁波315211

出　　处：《振动与冲击》2015年第6期127-131,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金(61071198);浙江省自然科学基金(LY13F010015);宁波市自然科学基金(2012A610019)

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。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 overcompleted 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.

关 键 词：多频信号 AR模型 稀疏表示 过完备稀疏基 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]