基于小波变换模改进Perona-Malik模型的强噪声信号滤波算法

PDF(957 KB)

振动与冲击 ›› 2018, Vol. 37 ›› Issue (17) : 277-282.

论文

毋文峰1，陈小虎2

作者信息 +

Strong noise signal filtering algorithm based on wavelet transform module and modified Perona-Malik model

WU Wenfeng1, CHEN Xiaohu2

Author information +

文章历史 +

摘要

鉴于偏微分方程在图像去噪中的原理和应用，针对传统机械振动信号去噪方法的局限性，提出了一种基于小波变换模改进Perona-Malik模型的强噪声信号滤波算法并用于机械振动信号去噪。首先研究了小波阈值去噪和Perona-Malik非线性各向异性扩散滤波模型之间的相关性，其次用小波变换模替代梯度模构建改进的扩散系数，并推导出了基于小波变换模的改进Perona-Malik模型。实验结果表明，与传统去噪方法和基本Perona-Malik模型相比，改进Perona-Malik模型不仅较好地实现了强噪声背景信号有效去噪，而且同时保留了信号细节特征，改进算法抗噪声干扰能力强，去噪之后信号畸变小，改进算法使信噪比平均提高了约3dB。

Abstract

Aiming at traditional mechanical vibration signals de-noising method’s limitation,considering partial differential equations’principle and application in image de-noising,a strong noise signal filtering algorithm based on wavelet transform module and modified Perona-Malik model was proposed. Firstly,the correlation between the wavelet threshold de-noising and Perona-Malik nonlinear anisotropic diffusion filtering model was studied. Secondly,wavelet transform module was used to substitute gradient module and construct an improved diffusion coefficient. The modified Perona-Malik model was derived based on wavelet transform module. The test results showed that compared with the traditional de-noising method and the basic Perona-Malik model,the modified Perona-Malik model can not only realize mechanical vibration signals’effective de-noising under strong noise background,but also keep signals’detail features with little signal distortion; it has a strong anti-noise capacity,the new algorithm makes the average SNR increase by about 3 dB.

导出引用

毋文峰1，陈小虎2. 基于小波变换模改进Perona-Malik模型的强噪声信号滤波算法[J]. 振动与冲击, 2018, 37(17): 277-282

WU Wenfeng1, CHEN Xiaohu2. Strong noise signal filtering algorithm based on wavelet transform module and modified Perona-Malik model[J]. Journal of Vibration and Shock, 2018, 37(17): 277-282

参考文献

[1] Donoho D. De-noising by soft thresholding [J]. IEEE Transactions on Information Theory, 1995, 41: 613-627.
[2] 包广清，常勇，杨国金. 基于EMD阈值方法的轴承故障振动信号去噪[J]. 计算机工程与应用，2015,51(10): 205-210.
BAO Guangqing, CHANG Yong, YANG Guojin. De-noising of rolling bearing fault vibration signal based on empirical mode decomposition threshold [J]. Computer Engineering and Applications, 2015,51(10): 205-210.
[3] 魏振春，王婿，徐娟. 基于改进阈值自适应冗余小波的振动信号去噪[J]. 计算机仿真，2014,31(11): 192-197.
WEI Zhenchun, WANG Xu, XU Juan. Denoising method of vibration signal based on improved threshold and adaptive redundant second generation wavelet [J]. Computer Simulation, 2014,31(11): 192-197.
[4] 苏祖强，萧红，张毅，等. 基于小波包分解与主流形识别的非线性降噪[J]. 仪器仪表学报，2016,37(9): 1954-1961.
SU Zuqiang, XIAO Hong, ZHANG Yi, et al.Nonlinear noise reduction method based on wavelet packet decomposition and principle manifold learning [J]. Chinese Journal of Scientific Instrucment, 2016,37(9): 1954-1961.
[5] 周祥鑫，王小敏，杨扬，等. 基于小波阈值的高速道岔振动信号降噪[J]. 振动与冲击，2014,33(23): 200-206.
ZHOU Xiangxin, WANG Xiaomin, YANG Yang, et al. De-noising of high-speed turnout vibration signals based on wavelet threshold [J]. Journal of Vibration and Shock, 2014,33(23): 200-206.
[6] 李红延，周云龙，田峰，等. 一种新的小波自适应阈值函数振动信号去噪算法[J]. 仪器仪表学报，2015,36(10): 2200-2206.
LI Hongyan, ZHOU Yunlong, TIAN Feng, et al. Wavelet-based vibration signal de-noising algorithm with a new adaptive threshpld function [J]. Chinese Journal of Scientific Instrucment, 2015,36(10): 2200-2206.
[7] 付海燕，吉小军，李兴旺. 基于TSA的直升机传动系统振动信号处理[J]. 计算机测量与控制， 2014,22(3): 930-931.
FU Haiyan, JI Xiaojun, LI Xingwang. TSA-based helicopter transmission system vibration signal processing [J]. Computer Measurement & Control, 2014,22(3): 930-931.
[8] 周晓峰，杨世锡，甘春标. 一种旋转机械振动信号的盲源分离消噪方法[J]. 振动、测试与诊断，2012,32(5): 714-717.
ZHOU Xiaofeng, YANG Shixi, GAN Chunbiao. De-noising vibration signal of rotating machinery with blind sources separation [J]. Journal of Vibration, Measurement & Diagnosis, 2012,32(5): 714-717.
[9] 隋文涛，张丹. 总变差降噪方法在轴承故障诊断中的应用[J]. 振动、测试与诊断，2014,34(6): 1033-1037.
SUI Wentao, ZHANG Dan. Total variation denoising method and its application in fault diagnosis of bearings [J]. Journal of Vibration, Measurement & Diagnosis, 2014,34(6): 1033-1037.
[10] Perona P, Malik J. Scale-space and edge detection using anisotropic diffusion [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990,12(7): 629-639.
[11] Catte F, Lions P L, Morel J, et al. Image selective smoothing and edge detection by nonlinear diffusion [J]. SIAM Journal on Numerical Analysis, 1992,29(3): 182-193.
[12] Ren Z, He C, Zhang Q. Fractional order total variation regularization for image super-resolution [J]. Signal Processing, 2013,93(9): 2408-2421.
[13] Liu Feng. Diffusion filtering in image processing based on wavelet transform [J]. Science in China Series F: Information Science, 2006,49(4): 494-503.
[14] 姜东焕，冯象初，宋国乡. 基于非线性小波阈值的各向异性扩散方程[J]. 电子学报，2006,34(1): 170-172.
JIANG Donghuan, FENG Xiangchu, SONG Guoxiang. An anisotropic diffusion equation based on nonlinear wavelet shrinkage [J]. Acta Electronica Sinica, 2006,34(1): 170-172.
[15] 刘晨华，冯象初. 基于连续状态小波阈值的各向异性扩散去噪方法[J]. 系统工程与电子技术，2009,31(4): 750-753.
LIU Chenhua, FENG Xiangchu. Denoising method of anisotropic diffusion based on continuous state wavelet threshold [J]. Systems Engineering and Electronics, 2009,31(4): 750-753.
[16] 陈利霞，丁宣浩，宋国乡，等. 基于总变分与小波变换的图像去噪算法[J]. 西安电子科技大学学报（自然科学版），2008,35(6): 1075-1079.
CHEN Lixia, DING Xuanhao, SONG Guoxiang, et al. Image de-noising algorithm based on total variation and wavelet transform [J]. Journal of XIDIAN University, 2008,35(6): 1075-1079.
[17] 吴宏钢，尹爱军，秦树人. 基于PDE的振动信号去噪[J]. 机械工程学报，2009,45(5): 91-94.
WU Honggang, YIN Aijun, QIN Shuren. Vibration signal denoising based on partial differential equation [J]. Journal of Mechanical Engineering, 2009,45(5): 91-94.
[18] 尹爱军，孙丽萍，王见. 偏微分方程在轴心轨迹提纯中的应用[J]. 重庆大学学报，2011,34(12): 72-77.
YIN Aijun, SUN Liping, WANG Jian. Purification of the shaft centerline orbit with partial differential equation [J]. Journal of Chongqing Unoversity, 2011,34(12): 72-77.
[19] 徐叶雷，黄青华，方勇. 一种基于偏微分方程的车辆加速度信号自适应降噪方法[J]. 传感器技术学报，2009,22(11): 1606-1611.
XU Yelei, HUANG Qinghua, FANG Yong. An adaptive de-noising method for vehicle’s acceleration signal based on PDE [J]. Chinese Journal of Sensors and Actuators, 2009,22(11): 1606-1611.
[20] Canny J. A computational approach to edge detection [J]. IEEE Transactions an Pattern Analysis and Machine Intelligence, 1986, 8(6): 679-698.