基于稀疏AR建模信号去噪研究与应用

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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。

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	宋欢欢
	叶庆卫
	王晓东
	周宇

关键词 ：多频信号, AR模型, 稀疏表示, 过完备稀疏基

Abstract：

The actual signal always contains noises by different surroundings and collected devices. And the noise has different forms. So the signal de-noise algorithm is a significant important pre-processing. The paper proposes a new de-noise algorithm which is based on sparse optimization. The algorithm assumes that coefficients of signal’s AR model are sparse and the impact of noise effect on coefficient of AR model is equilibrium distribution. A sparse AR model is built by the signal with noises. The AR coefficients matrix is created by noised signal. Take the matrix as the over-completed sparse basis. One underdetermined equation set is obtained by cramped out some rows from the over-completed sparse basis randomly. Then the sparse AR coefficients are solved by sparse optimization algorithm. And the above processing is repeated many times to obtain many sparse AR coefficients. At last, the AR coefficients are averaged, and the de-noised signal is reconstructed by the averaged AR coefficients. A bidirectional algorithm is proposed by the above de-noise algorithm. The original signal and its inversion signal are de-noised and averaged. For general multi-frequency signals with lager noises, many simulation experiments are tested. It indicates that the de-noising effect obtained by using the algorithm in this paper is better than the classical wavelet de-noising algorithm and median filtering de-noising algorithm. The algorithm in this paper is applied to de-noising step for the vibration signal of the bridge cable, and practice shows that algorithm in this paper has excellent effect.

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

收稿日期: 2013-10-21 出版日期: 2015-03-25

引用本文:

宋欢欢，叶庆卫，王晓东，周宇. 基于稀疏AR建模信号去噪研究与应用[J]. 振动与冲击, 2015, 34(6): 127-131.
SONG Huan-huan，YE Qing-wei，WANG Xiao-dong，ZHOU Yu. A new algorithm of signal de-noising based on sparse AR model. JOURNAL OF VIBRATION AND SHOCK, 2015, 34(6): 127-131.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2015/V34/I6/127

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