针对软阈值和硬阈值去噪算法存在的缺陷,提出了一种基于高斯性检验的自适应非线性阈值去噪方法。该方法根据信号和噪声的模极大值特性自适应确定分解层数,引入高斯性检验选择软阈值和硬阈值方法对每层小波系数进行降噪处理。仿真结果表明,该自适应滤波方法简单有效、稳定性高,去噪后信号信噪比得到很大提高,且不同仿真信号结果都明显优于经典的小波去噪算法。
Abstract
Based on the known defects of soft thresholding and hard thresholding, an adaptive nonlinear threshold denoising method based on Gaussian tests has been proposed. The new method adaptively determines the decomposition level according to the characteristics of signal and noise for wavelet coefficients of each level, choosing soft and hard thresholding methods to deal with it through Gaussian tests. The experimental results show that the method is effective, the signal-to-noise ratio is highly improved, and the results are superior to the classical wavelet denoising algorithm for different simulated signals, resulting in much higher stability.
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1]王维,张英堂,任国全. 小波阈值降噪算法中最优分解层数的自适应确定及仿真[J]. 仪器仪表学报, 2009, 30(3): 526-〖JP〗530.
Wang W, Zhang Y T, Ren G Q. Adaptive selection and simulation of optimal decomposition level in threshold de-noising algorithm based on wavelet transform[J]. Chinese Journal of Scientific Instrument, 2009, 30(3): 526-〖JP〗530. (in Chinese)
[2]郑成博,阎洪涛,刘彬,等. 基于Grubbs 准则的小波自适应阈值去噪算法[J]. 仪器仪表学报,2005,26(8):107-108.
Zheng C B, Yan H T, Liu B, et al.Wavelet thresholding denoising algorithm based on adaptive decomposition[J]. Chinese Journal of Scientific Instrument, 2005, 26(8): 107-108. (in Chinese)
[3]滕军,朱焰煌, 周峰,等. 自适应分解层数的小波域中值滤波振动信号降噪法[J]. 振动与冲击,2009,28(12):58-62.
Teng J, Zhu Y H, Zhou F, et al. Vibration signal denoising method based on median filter in wavelet domain with self-adaptive level decomposition[J]. Journal of Vibration and Shock, 2009, 28(12): 58-62. (in Chinese)
[4]Gao H Y. Wavelet shrinkage denoising using the non-negative garrotte[J]. Journal of Computational and Graphical Statistics, 1998, 7(4): 469-488.
[5]蒋克荣,唐向清,朱德泉. 基于改进阈值小波算法的汽车轮速信号处理[J]. 仪器仪表学报,2010,31(4):736-740.
Jiang K R, Tang X Q, Zhu D Q. Automobile wheel speed signal processing based on wavelet algorithm of improved threshold[J]. Chinese Journal of Scientific Instrument, 2010, 31(4): 736-740. (in Chinese)
[6]Nasri M, Nezamabadi pour H. Image denoising in the wavelet domain using a new adaptive thresholding function[J]. Neurocomputing, 2009, 72(4/5/6):1012-1025.
[7]Yang R G, Ren M W.Wavelet denoising using principal component analysis[J]. Expert Systems with Applications, 2011, 38(1): 1073-1076.
[8]Chen X J, Wu C G, Zhu X G. Optimization of wavelet functions for wavelet thresholding denoising[J]. Energy Procedia, 2011, 13: 3440-3444.
[9]Donoho D L. De-noising by soft-thresholding[J]. IEEE Transactions on Information Theory, 1995, 41(3): 613-627.
[10]Millioz F, Martin N. Circularity of the STFT and spectral kurtosis for time-frequency segmentation in gaussian environment[J]. IEEE Transactions on Signal Processing, 2011, 59(2): 515-524.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}