不同信号的小波变换去噪方法
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摘要
本文介绍了小波分解与重构、小波变换阈值及小波变换模极大值三种常用的小波去噪方法,并将上述三种方法分别对叠加了高斯白噪声的仿真信号进行去噪处理。对三种方法的优缺点进行了比较和分析,结果表明:对于信号和噪声的频带相互分离的含有确定性噪声的信号,选用方法简单、计算速度快的小波分解与重构去噪法最为合适;对于含有高斯白噪声的信号,可以选用阈值法和模极大值法。由于阈值法具有能得到原始信号的近似最优估计、计算速度快以及具有广泛的适应性等优点,因而成为小波去噪方法中应用最广泛的一种去噪方法。小波变换模极大值法对于信号中含有较多的奇异点的信号去噪效果最好,但其缺点是计算速度慢。在实际应用中需权衡去噪效果和计算速度之间的关系,有效、合理地选择最适合实际资料的去噪方法。
The paper introduced three common-used de-noise approaches by wavelet; wavelet decomposition and reconstruction,threshold of wavelet transform and modular extreme of wavelet transform. The denoise processing is carried out by abovementioned approaches for simulated signals adding Gauss white noise respectively,and correlation and analysis of advantages and disadvantages of these three approaches showed that it is suitable to select wavelet decomposition and reconstruction as denoise approach that is characterized by simple method and rapid computational speed when the denoise processing is carried out for the signals with band-separated signal and noise and determinable noise; the threshold and modular extreme approaches can be selected for the denoise processing of Gauss white-noise-bearing signals. Since the threshold approach is characterized by obtaining the approximate optimum evaluation of original signal,rapid computational speed and wide adaptability, which is most popular-used denoise approach among the wavelet denoise methods. The modular extreme approach of wavelet transform has better denoise effects for the signals containing more singularities, but its disadvantage is slow computational speed. It should strike a balance between the denoise effect and computational speed and effectively and reasonably select the denoise approach that is suitable for the practical data when practically using wavelet transform for denoise.
The paper introduced three common-used de-noise approaches by wavelet; wavelet decomposition and reconstruction,threshold of wavelet transform and modular extreme of wavelet transform. The denoise processing is carried out by abovementioned approaches for simulated signals adding Gauss white noise respectively,and correlation and analysis of advantages and disadvantages of these three approaches showed that it is suitable to select wavelet decomposition and reconstruction as denoise approach that is characterized by simple method and rapid computational speed when the denoise processing is carried out for the signals with band-separated signal and noise and determinable noise; the threshold and modular extreme approaches can be selected for the denoise processing of Gauss white-noise-bearing signals. Since the threshold approach is characterized by obtaining the approximate optimum evaluation of original signal,rapid computational speed and wide adaptability, which is most popular-used denoise approach among the wavelet denoise methods. The modular extreme approach of wavelet transform has better denoise effects for the signals containing more singularities, but its disadvantage is slow computational speed. It should strike a balance between the denoise effect and computational speed and effectively and reasonably select the denoise approach that is suitable for the practical data when practically using wavelet transform for denoise.
引文
[1]黄德济,贺振华,包吉山．地震勘探资料数字处理．北京:地质出版社,1990
[2]李庆忠．走向精确勘探的道路．北京:石油工业出版社,1993
[3]谭毅华,田金文,柳健。基于小波局部统计特性的图像去噪方法．信号处理,2005
[4]成礼智,王红霞,罗永．小波的理论与应用．北京:科学出版社,2004
[5]梁学章,何甲兴等．小波分析．北京:国防工业出版社, 2004
[6]李建平,唐远炎．小波分析方法的应用．重庆:重庆大学出版社,1999
[7]李世雄．小波变换及其应用．北京:高等教育出版社, 1997
[8]胡广书．数字信号处理——理论、算法与实现．北京:清华大学出版社,1997
[9] MATLAB 6．5辅助小波分析与应用．北京:电子工业出版社,2003
[10]Donoho D．De-noising by soft-thresholding．IEEE Trans On IT,1995,3,613～627
[2]李庆忠．走向精确勘探的道路．北京:石油工业出版社,1993
[3]谭毅华,田金文,柳健。基于小波局部统计特性的图像去噪方法．信号处理,2005
[4]成礼智,王红霞,罗永．小波的理论与应用．北京:科学出版社,2004
[5]梁学章,何甲兴等．小波分析．北京:国防工业出版社, 2004
[6]李建平,唐远炎．小波分析方法的应用．重庆:重庆大学出版社,1999
[7]李世雄．小波变换及其应用．北京:高等教育出版社, 1997
[8]胡广书．数字信号处理——理论、算法与实现．北京:清华大学出版社,1997
[9] MATLAB 6．5辅助小波分析与应用．北京:电子工业出版社,2003
[10]Donoho D．De-noising by soft-thresholding．IEEE Trans On IT,1995,3,613～627
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