基于多假设检验的新型小波滤波算法

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振动与冲击 ›› 2011, Vol. 30 ›› Issue (7) : 197-200.

论文

基于多假设检验的新型小波滤波算法

杜文辽1,2; 刘成良1; 李彦明1

作者信息 +

The threshold for wavelet de-noising based on multiple hypothesis test

Du Wen-liao1,2; Liu Cheng-liang1; Li Yan-ming1

Author information +

文章历史 +

摘要

小波阈值滤波是信号处理领域的重要方法，根据信号和白噪声在小波空间上传播的特性，提出了一种基于多假设检验确定小波滤波阈值的新算法。将小波阈值处理过程看作一个多重假设检验过程，FDR（False Discovery Rate）准则的step-up和step-down过程均能控制FDR在给定的显著性水平，综合这两个过程形成了FDR step-up-down过程并应用于确定小波滤波阈值。仿真实验表明，算法能够灵活调整显著性水平的大小来达到滤波后所希望的效果，以信噪比和均方误差作为衡量指标，本方法滤波效果与hearsure方法相当，优于BH FDR及sqtwolog方法。讨论了显著性水平的选取对滤波效果的影响，指出显著性水平的大小与信噪比的改善并非线性关系，提出了合理选取显著性水平的思路。

Abstract

Threshold de-noising method based on the wavelet transform is an effective approach to reduce the white noise in the digit signal. Considering the different characters of signal and white noise in the wavelet domain, a novel algorithm to determine the wavelet threshold is proposed with the multiple hypothesis test. Since the wavelet de-noising transform process can be regarded as a multiple hypothesis process and both the step-up and step-down procedure can control the FDR, the new method FDR step-up-down procedure combining the above-mentioned procedures determines the wavelet threshold. An attractive advantage of this method is it can obtain the desired result by adjusting the FDR level flexibly. The simulated numerical results show that this method works as effective as hearsure method and gives better SNR gains and MSE performance than both the traditional BH FDR and sqtwolog method. The selection of the significance level is also discussed, and point out that the relationship between the significant level and the improvement of the signal to noise ratio is nonlinear, then the tactic of selecting the proper significant level is proposed.

导出引用

杜文辽; 刘成良; 李彦明 . 基于多假设检验的新型小波滤波算法[J]. 振动与冲击, 2011, 30(7): 197-200

Du Wen-liao; Liu Cheng-liang;Li Yan-ming. The threshold for wavelet de-noising based on multiple hypothesis test[J]. Journal of Vibration and Shock, 2011, 30(7): 197-200