基于最优小波包基的降噪方法及其应用
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摘要
如何有效去除信号中的噪声是地球物理勘探领域中一个较重要的研究内容。如何去除有效数据中的噪声而保持信号的初至相位不发生畸变,常规的频率域或时间域滤波方法均不能较好的解决这个问题,而基于小波包基的信号去噪方法却是一种较好的方法。本文以小波包分析为基础,根据最小代价原理研究信号分解的最佳小波包基,对不同频率的系数采用不同的阈值进行量化,对高频信号采用Stein无偏似然估计的原则计算阈值,而在低频部分则采用以信号能为依据的浮动阈值,利用量化后的小波包系数重构得到去噪后的信号。仿真和实验结果表明,该方法去除噪声的同时并不改变原信号的相位,也不会产生波形的畸变。同时,将该方法利用到超声波数据降噪处理的工程实际中也取得了较好的效果。
How to denoise effectively is a more important research subject in geophysical exploration field.The conventional frequency domain and time domain filtering methods cannot effectively extract the signal from the noised data without changing the first phase of signal,but the wavelet packet decomposition method could do it better.The algorithm based on wavelet packets decomposition which bases on wavelet packet analysis and looks for the best groups of signal analysis for least costs principle.In this paper,disturbed signal was decomposed into the multiscale wavelet domain by minimal Shannon entropy criteria.Then,the threshold based on Stein's unbiased risk estimation was used to eliminate the noise in the high frequency coefficients and little energy losses were used to set the threshold of the low frequency coefficients.Finally,the denoised signal was achieved by the invert wavelet packet decomposition.The experimental results show that this method can effectively get the correct signal feature and do not change the phase of original signal and it is an ideal method to get ride of the white noise from our interested signal.
How to denoise effectively is a more important research subject in geophysical exploration field.The conventional frequency domain and time domain filtering methods cannot effectively extract the signal from the noised data without changing the first phase of signal,but the wavelet packet decomposition method could do it better.The algorithm based on wavelet packets decomposition which bases on wavelet packet analysis and looks for the best groups of signal analysis for least costs principle.In this paper,disturbed signal was decomposed into the multiscale wavelet domain by minimal Shannon entropy criteria.Then,the threshold based on Stein's unbiased risk estimation was used to eliminate the noise in the high frequency coefficients and little energy losses were used to set the threshold of the low frequency coefficients.Finally,the denoised signal was achieved by the invert wavelet packet decomposition.The experimental results show that this method can effectively get the correct signal feature and do not change the phase of original signal and it is an ideal method to get ride of the white noise from our interested signal.
引文
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[2]戎丽霞.基于最优小波包基的信号去噪算法[J].德州学院学报,2005,21(2):72~75.
[3]S Mallat,Z Zhang.Matching pursuit with time-fre-quency dictionaries[J].IEEE Transactions on Sig-nal Processing,1993,41(12):3397~3415.
[4]徐亚,郝天珧.提升小波:可用于重磁资料处理的新方法[J].地球物理学进展,2004,19(1):36~39.
[5]柳建新,韩世礼,马捷.小波分析在地震资料去噪中的应用[J].地球物理学进展,2006,21(2):541~545.
[6]I Daubechies.Ten Lectures on Wavelets[R].SIAM,Philadelphia,PA,1992.
[7]高印寒,马喜来,何丽桥,等.基于小波包分解的阈值消噪在车载CAN总线上的应用[J].光学精密工程,2007,15(3):434~439.
[8]索进章,梁昭峰,董守龙,等.小波阈值去噪法在超声信号处理中的应用研究[J].噪声与振动控制,2006,6(3):35~38.
[9]魏云冰,黄进,黄建华.基于小波包变换的电机测试信号去噪处理[J].电工技术学报,2001,16(5):64~67.
[2]戎丽霞.基于最优小波包基的信号去噪算法[J].德州学院学报,2005,21(2):72~75.
[3]S Mallat,Z Zhang.Matching pursuit with time-fre-quency dictionaries[J].IEEE Transactions on Sig-nal Processing,1993,41(12):3397~3415.
[4]徐亚,郝天珧.提升小波:可用于重磁资料处理的新方法[J].地球物理学进展,2004,19(1):36~39.
[5]柳建新,韩世礼,马捷.小波分析在地震资料去噪中的应用[J].地球物理学进展,2006,21(2):541~545.
[6]I Daubechies.Ten Lectures on Wavelets[R].SIAM,Philadelphia,PA,1992.
[7]高印寒,马喜来,何丽桥,等.基于小波包分解的阈值消噪在车载CAN总线上的应用[J].光学精密工程,2007,15(3):434~439.
[8]索进章,梁昭峰,董守龙,等.小波阈值去噪法在超声信号处理中的应用研究[J].噪声与振动控制,2006,6(3):35~38.
[9]魏云冰,黄进,黄建华.基于小波包变换的电机测试信号去噪处理[J].电工技术学报,2001,16(5):64~67.
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