李 文 刘 霞 段玉波 姚建红 刘继承 潘洪屏. 2012: 基于小波熵与相关性相结合的小波模极大值地震信号去噪. 地震学报, 34(6): 841-850.
引用本文: 李 文 刘 霞 段玉波 姚建红 刘继承 潘洪屏. 2012: 基于小波熵与相关性相结合的小波模极大值地震信号去噪. 地震学报, 34(6): 841-850.
Li Wen Liu Xia Duan Yubo Yao Jianhong Liu Jicheng Pan Hongping. 2012: Wavelet modulus maxima denoising of seismic signals based on combined wavelet entropy and correlation. Acta Seismologica Sinica, 34(6): 841-850.
Citation: Li Wen Liu Xia Duan Yubo Yao Jianhong Liu Jicheng Pan Hongping. 2012: Wavelet modulus maxima denoising of seismic signals based on combined wavelet entropy and correlation. Acta Seismologica Sinica, 34(6): 841-850.

基于小波熵与相关性相结合的小波模极大值地震信号去噪

Wavelet modulus maxima denoising of seismic signals based on combined wavelet entropy and correlation

  • 摘要: 小波模极大值去噪算法中将高频小波系数全部当做噪声处理, 忽略了高频小波系数中仍含有的有用信息, 从而导致了模极大值传播点错选现象以及计算出的噪声方差中仍含有用信息. 针对这些问题, 提出了小波熵与相关性相结合的小波模极大值去噪算法. 将高频小波系数进行相关处理, 确定有效信号的位置; 将最大尺度上的高频小波系数划分成若干个小区间, 计算各区间小波熵; 以小波熵最大区间的高频小波系数的平均值作为噪声方差, 根据Donoho提出的阈值公式计算最大尺度上的阈值; 经阈值比较得到的模极大值点位置与相关处理得到的有用信息的位置进行比较, 保留相同位置的模极大值, 剔除位置不同由噪声引起的模极大值点; 采用即兴(Adhoc)算法逐级搜索各尺度上的模极大值, 并用交替投影算法进行重构. 该算法实现了阈值的自适应选取, 并有效解决了去除错选模极大值传播点的问题. 将本算法和传统去噪方法用于仿真信号处理中, 经对比分析验证了本算法的有效性.

     

    Abstract: In wavelet modulus maxima denoising algorithms, high-frequency wavelet coefficients are all considered as noises, and the useful information in them is ignored, therefore, modulus maxima pickup points are wrongly selected and the calculated noise variances still contain useful information. To solve these problems, this paper proposed a wavelet modulus maxima denoising algorithm which combines wavelet entropy with correlation. The effective signal location is determined by correlation processing of high-frequency wavelet coefficients. The high-frequency wavelet coefficients on the maximum scale are divided into several small zones, and the interval wavelet entropy is calculated. With the mean value of high-frequency wavelet coefficients in the wavelet entropy maxima interval as noise variance, the threshold value of the maxima scale is calculated according to the formula presented by Donoho in 1995. By comparing locations of the maxima point obtained by comparison the threshold values with locations of the useful information obtained by correlation processing, the modulus maxima of the same position are retained and modulus maxima points of different positions caused by noises are eliminated. The modulus maxima of each level are searched with the Adhoc algorithm step by step and the denoised signals are reconstructed by alternating projection algorithm. This improved algorithm realized adaptive selection of threshold values and removal of wrongly selected modulus maxima pickup points. Our method and a conventional denoising method were both applied to simulation signal processing, and comparative analysis verified effectiveness of our improved method.

     

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