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
|
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.
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.
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.
引文
陈德智,唐磊,盛剑霓,王恒利.1998.由小波变换的模极大值快速重构信号[J].电子学报,26(9):82--85.
段炜.2008.基于小波变换的探地雷达信号去噪方法研究[D].长沙:中南大学:43--54.
姜弢,刘庆普,胡留军.2002.地震信号去噪的小波方法研究[J].哈尔滨工程大学学报,23(4):86--89.
蒋鹏.2004.小波理论在信号去噪和数据压缩的应用研究[D].杭州:浙江大学:47--59.
孔祥茜,吴继伟,岳继光.2005.地震信号小波变换的去噪方法[J].计算机辅助工程,14(3):52--56.
李华.2000.小波理论分析及其在地震信号处理中的应用研究[D].成都:成都理工学院:43--52.
陆基孟.2005.地震勘探原理下册[M].北京:石油大学出版社:312--328.
潘洪屏.2011.基于小波分析技术的地震信号去噪方法研究[D].大庆:东北石油大学:38--40.
孙丰荣,翟广涛,李艳玲,刘泽,张梅,张运.2005.由小波变换模极大值重构信号的快速算法[J].小型微型计算机系统,26(12):2147--2149.
孙延奎.2005.小波分析及其应用[M].北京:机械工业出版社:224--236.
田金文,高谦,杜拥军.2001.基于小波变换模极大值的地震信号去噪处理方法[J].江汉石油学院学报,23(1):22--25.
王秀明.2007.应用地球物理方法原理[M].北京:石油工业出版社:23--25.
徐长发,李国宽.2004.实用小波方法[M].武汉:华中科技大学出版社:107--119.
姚胜利.2007.地震信号的小波去噪方法研究[D].长沙:中南大学:22--37.
张荣标,胡海燕,冯友兵.2007.基于小波熵的微弱信号检测方法研究[J].仪器仪表学报,28(11):2078--2083.
张媛玲.2001.小波分析在地震勘探资料处理中的应用[D].沈阳:沈阳工业大学:12--14,34--43.
周怀来.2006.基于小波变换的地震信号去噪方法研究与应用[D].成都:成都理工大学:1--7.
朱晓明.2007.工程地震信号去噪技术研究[D].青岛:中国海洋大学:1--14.
Alnashash H A,Paul J S.2003.Wavelet entropy method for EEG analysis application to global brain injury[C]∥IEEEEMBS Conference on Neural Engineering.Capri Island,Italy.3:348--351.
Donoho D.1995.De-noising by soft-thresholding[J].IEEE Trans on IT,3:613--627.
He Z Y,Cai Y M.2004.A study of wavelet entropy theory and its application in power system[C]∥IEEE InternationalConference on Intelligent Mechatronics and Automation.Chengdu,China.8:847--851.
Hsung T C,Lun D P K.1999.Denoising by singularity detection[J].IEEE Transactions on Signal Processing,47(11):3139--3144.
Mallat S G,Zhong S.1992.Characterization of signals from multiscale edges[J].IEEE Transactions on PatternAnalysis and Machine Intelligence,14(7):710--732.
Witkin A P.1983.Scale space filtering[C]∥Proceedings of the Eighth International Joint Conference on Artificial Intelligence.Karlsruhe,Germany:1019--1022.
Ykhlef F,Arezki M.2004.A wavelet denoising method to improve detection with ultrasonic signal[C]∥IEEE International Conference on Industrial Technology.Hammamet,Tunisia:1422--1425.
段炜.2008.基于小波变换的探地雷达信号去噪方法研究[D].长沙:中南大学:43--54.
姜弢,刘庆普,胡留军.2002.地震信号去噪的小波方法研究[J].哈尔滨工程大学学报,23(4):86--89.
蒋鹏.2004.小波理论在信号去噪和数据压缩的应用研究[D].杭州:浙江大学:47--59.
孔祥茜,吴继伟,岳继光.2005.地震信号小波变换的去噪方法[J].计算机辅助工程,14(3):52--56.
李华.2000.小波理论分析及其在地震信号处理中的应用研究[D].成都:成都理工学院:43--52.
陆基孟.2005.地震勘探原理下册[M].北京:石油大学出版社:312--328.
潘洪屏.2011.基于小波分析技术的地震信号去噪方法研究[D].大庆:东北石油大学:38--40.
孙丰荣,翟广涛,李艳玲,刘泽,张梅,张运.2005.由小波变换模极大值重构信号的快速算法[J].小型微型计算机系统,26(12):2147--2149.
孙延奎.2005.小波分析及其应用[M].北京:机械工业出版社:224--236.
田金文,高谦,杜拥军.2001.基于小波变换模极大值的地震信号去噪处理方法[J].江汉石油学院学报,23(1):22--25.
王秀明.2007.应用地球物理方法原理[M].北京:石油工业出版社:23--25.
徐长发,李国宽.2004.实用小波方法[M].武汉:华中科技大学出版社:107--119.
姚胜利.2007.地震信号的小波去噪方法研究[D].长沙:中南大学:22--37.
张荣标,胡海燕,冯友兵.2007.基于小波熵的微弱信号检测方法研究[J].仪器仪表学报,28(11):2078--2083.
张媛玲.2001.小波分析在地震勘探资料处理中的应用[D].沈阳:沈阳工业大学:12--14,34--43.
周怀来.2006.基于小波变换的地震信号去噪方法研究与应用[D].成都:成都理工大学:1--7.
朱晓明.2007.工程地震信号去噪技术研究[D].青岛:中国海洋大学:1--14.
Alnashash H A,Paul J S.2003.Wavelet entropy method for EEG analysis application to global brain injury[C]∥IEEEEMBS Conference on Neural Engineering.Capri Island,Italy.3:348--351.
Donoho D.1995.De-noising by soft-thresholding[J].IEEE Trans on IT,3:613--627.
He Z Y,Cai Y M.2004.A study of wavelet entropy theory and its application in power system[C]∥IEEE InternationalConference on Intelligent Mechatronics and Automation.Chengdu,China.8:847--851.
Hsung T C,Lun D P K.1999.Denoising by singularity detection[J].IEEE Transactions on Signal Processing,47(11):3139--3144.
Mallat S G,Zhong S.1992.Characterization of signals from multiscale edges[J].IEEE Transactions on PatternAnalysis and Machine Intelligence,14(7):710--732.
Witkin A P.1983.Scale space filtering[C]∥Proceedings of the Eighth International Joint Conference on Artificial Intelligence.Karlsruhe,Germany:1019--1022.
Ykhlef F,Arezki M.2004.A wavelet denoising method to improve detection with ultrasonic signal[C]∥IEEE International Conference on Industrial Technology.Hammamet,Tunisia:1422--1425.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心