改进的多小波变换系数相关去噪算法
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摘要
多小波变换系数在同一尺度上具有多个输出块,传统的多小波系数相关去噪算法只利用了尺度间或同一尺度上相同块内相邻变换系数之间的相关性;为了改善去噪效果,根据白噪声和信号的多小波变换系数的不同特性,将同一尺度上不同块的变换系数做相关运算及归一化后分别与原来块的变换系数进行比较,根据相应的规则对变换系数进行取舍,然后再采用"相邻系数法"对保留的变换系数进行处理,进一步地去除噪声。由于同时考虑了同一尺度上不同块之间和相同块内相邻变换系数之间的相关性,仿真和实验结果表明该方法能够更好地减少噪声对小波变换系数的干扰,突显出信号突变点的小波变换系数,具有更好的去噪效果。
When a signal is decomposed by multiwavelet,the multiwavelet coefficient consists of several blocks,and the correlation of coefficients in same blocks or cross the scales is utilized to denoise the signal usually.According to the different characteristics of signal and white noise,we put forward a denoising algorithm based on the correlation of multiwavelet coefficients for the better denoising performance.Firstly,we calculated the correlative coefficient of different blocks.Then,we compared the correlative coefficient with normalized correlative coefficient and made selection according to the rule,in which the reserved correlative coefficient was processed with neighboring coefficient method.Using the algorithm,the correlation of neighboring coefficients and different blocks was taken into account simultaneously.So the denoising performance was better than that of the conventional algorithm which only adopted the neighboring coefficients.The experimental results show that the interference of noise is reduced,and the break point is more visible.
When a signal is decomposed by multiwavelet,the multiwavelet coefficient consists of several blocks,and the correlation of coefficients in same blocks or cross the scales is utilized to denoise the signal usually.According to the different characteristics of signal and white noise,we put forward a denoising algorithm based on the correlation of multiwavelet coefficients for the better denoising performance.Firstly,we calculated the correlative coefficient of different blocks.Then,we compared the correlative coefficient with normalized correlative coefficient and made selection according to the rule,in which the reserved correlative coefficient was processed with neighboring coefficient method.Using the algorithm,the correlation of neighboring coefficients and different blocks was taken into account simultaneously.So the denoising performance was better than that of the conventional algorithm which only adopted the neighboring coefficients.The experimental results show that the interference of noise is reduced,and the break point is more visible.
引文
[1]Donoho D,Johnstone I M.Ideal special adaption by waveletshrinkage[J].Biopmetrika,1995,81(3):425-455.
[2]Geronimo J S,Hardin D P,Massopust P R.Fractal functionsand wavelet expansions based on several functions[J].J ApproxTheory,1994,78(3):373-401.
[3]Xia X G,Geronimo J S,Hardin Douglas P,et al.Design of pre-filters for discrete multiwavelet transforms[J].IEEE Transac-tions on Signal Processing,1996,44(1):25-34.
[4]Donvan G C,Geronimo J S,Hardin D P,et al.Construction oforthogonal wavelets using fractal interpolation function[J].So-ciety for Industrial and Applied Mathematics Journal on Mathe-matical Analysis,1996,27(4):1158-1192.
[5]刘军,张晓威.一种新的正交多小波函数的构造[J].山东大学学报(理学版),2009,44(12):85-90.LIU Jun,ZHANG Xiao-wei.A new method for construction oforthogonal multiwavelets functions[J].Journal of Shandong U-niversity(Natural Science),2009,44(12):85-90.
[6]罗辉,邓彩霞,徐延新.一种二维正交多小波的构造方法[J].哈尔滨理工大学学报,2009,14(5):107-109.LUO Hui,DENG Cai-xia,XU Yan-xin.An approach of con-structing bivariate orthogonal multiwavelet[J].Journal of Har-bin University of Science and Technology,2009,14(5):107-109.
[7]赵英敏,黄永东.区间多小波的构造及其平衡性刻画[J].宁夏大学学报(自然科学版),2010,31(1):1-4.ZHAO Ying-min,HUANG Yong-dong.Construction and bal-ancing characterization of interval multiwavelets[J].Journal ofNingxia University(Natural Science Edition),2010,31(1):1-4.
[8]曾朝晖.正交对称多小波构造及其图像压缩仿真研究[J].系统仿真学报,2010,22(5),1246-1250.ZENG Zhao-hui.Construction of orthogonal symmetric multi-wavelets and simulation in image compression[J].Journal ofSystem Simulation,2010,22(5),1246-1250.
[9]唐惠玲,刘志军.多小波变换在电能质量扰动检测与分类中的应用[J].江西师范大学学报(自然科学版),2009,33(2):148-152.TANG Hui-ling,LIU Zhi-jun.The application of multiwavelettransformation in power quality disturbance detetction and clas-sification[J].Journal of Jiangxi Normal University(Natural Sci-ence),2009,33(2):148-152.
[10]高太长,韩小冬,邱实,等.基于多小波变换的电场变化仪信号去噪[J].解放军理工大学学报(自然科学版),2009,10(增刊):90-94.GAO Tai-chang,HAN Xiao-dong,QIU Shi,et al.Electric-field changes meter signal de-noising based on multi-wavelettransform[J].Journal of PLA University of Science and Tech-nology(Natural Science Edition),2009,10(Supplement):90-94.
[11]农京辉,王锦莉,刘爱林,等.利用多小波的改进多层阈值对超声图像降噪[J].计算机工程与应用,2009,45(22):138-143.NONG Jing-hui,WANG Jin-li,LIU Ai-lin,et al.Ultrasoundimage de-noising using modified multilevel threshold[J].Com-puter Engineering and Applications,2009,45(22):138-143.
[12]戴庆,卢杨,栗磊.基于多小波自适应阈值的地震图像去噪方法[J].科学技术与工程,2009,9(24):7533-7536.DAI Qing,LU Yang,LI Lei.Based on many wavelelt adaptivethreshold image denoising method of earthquake[J].ScienceTechnology and Engineering,2009,9(24):7533-7536.
[13]张蕊,王学伟,王琳.基于GHM多小波的电力系统故障录波数据压缩算法[J].电测与仪表,2008,45(10):46-50.ZHANG Rui,WANG Xue-wei,WANG Lin.Compression al-gorithm of fault recording data in power system based on GHMmultiwavelet[J].Electrical Measurement&Instrumentation,2008(5),45(10):46-50.
[14]胡海平.基于广义交叉认证的多小波阈值的图像降噪[J].应用数学与计算机数学学报,2009,23(1):61-65.HU Hai-ping.A multiwavelet threshold image denoising basedon general cross-validation[J].Communication on AppliedMathematics and Computation,2009,23(1):61-65.
[15]Downie T R,Sliverman B W.The discrete multiple wavelettransform and thresholding methods[J].IEEE Transactions onSignal Processing,1998,46(9):2558-2561.
[16]Strela V,Heller P N,Topiwala P,et al.The application ofmulti-wavelet filter banks to image processing[J].IEEETransactions on Image Processing,1999,8(4):548-563.
[17]刘志刚,钱清泉.自适应阈值多小波故障暂态信号去噪方法[J].系统工程与电子技术,2004,26(7):878-880.LIU Zhi-gang,QIAN Qing-quan.Adaptive shrinkage value de-noi-sing method of fault transient signals with multiwavelets[J].Sys-tems Engineering and Electronics,2004,26(7):878-880.
[18]谢荣生,李汉杰,孙枫,等.基于多小波噪声方差阈值的信号滤波方法[J].哈尔滨工程大学学报,2002,23(2):51-54.XIE Rong-sheng,LI Han-jie,SUN Feng,et al.Filtering algo-rithm based on multiwavelet noise variance threshold[J].Jour-nal of Harbin Engineering University,2002,23(2):51-54.
[19]刘志刚,曾怡达,钱清泉.多小波在电力系统信号消噪中的应用[J].中国电机工程学报,2004,24(1):30-34.LIU Zhi-gang,ZENG Yi-da,QIAN Qing-quan.Denoising ofelectric power system signals based on different multiwavelets[J].Proceedings of the CSEE,2004,24(1):30-34.
[20]Chen G Y,Bui T D.Multiwavelets denoising using neighboringcoefficients[J].IEEE Signal Processing Letters,2003,10(7):211-214.
[21]Cai T T,Silverman B W.Incorporating information on neigh-boring coefficients into wavelet estimation[J].Indian Journalof Statistics B,2001,63(2):127-148.
[22]卢恩博,陈俊丽,黄炳.一种改进的多小波相邻系数去噪算法[J].计算机仿真,2008,25(5):321-323.LU En-bo,CHEN Jun-li,HUANG Bing.An improved multi-wavelet denoising method using neighboring coefficients[J].Computer Simulation,2008,25(5):321-323.
[23]Bui T D,Chen G.Translation-invariant denoising using multi-wavelets[J].IEEE Transactions on Signal Processing,1998,46(12):3414-3420.
[2]Geronimo J S,Hardin D P,Massopust P R.Fractal functionsand wavelet expansions based on several functions[J].J ApproxTheory,1994,78(3):373-401.
[3]Xia X G,Geronimo J S,Hardin Douglas P,et al.Design of pre-filters for discrete multiwavelet transforms[J].IEEE Transac-tions on Signal Processing,1996,44(1):25-34.
[4]Donvan G C,Geronimo J S,Hardin D P,et al.Construction oforthogonal wavelets using fractal interpolation function[J].So-ciety for Industrial and Applied Mathematics Journal on Mathe-matical Analysis,1996,27(4):1158-1192.
[5]刘军,张晓威.一种新的正交多小波函数的构造[J].山东大学学报(理学版),2009,44(12):85-90.LIU Jun,ZHANG Xiao-wei.A new method for construction oforthogonal multiwavelets functions[J].Journal of Shandong U-niversity(Natural Science),2009,44(12):85-90.
[6]罗辉,邓彩霞,徐延新.一种二维正交多小波的构造方法[J].哈尔滨理工大学学报,2009,14(5):107-109.LUO Hui,DENG Cai-xia,XU Yan-xin.An approach of con-structing bivariate orthogonal multiwavelet[J].Journal of Har-bin University of Science and Technology,2009,14(5):107-109.
[7]赵英敏,黄永东.区间多小波的构造及其平衡性刻画[J].宁夏大学学报(自然科学版),2010,31(1):1-4.ZHAO Ying-min,HUANG Yong-dong.Construction and bal-ancing characterization of interval multiwavelets[J].Journal ofNingxia University(Natural Science Edition),2010,31(1):1-4.
[8]曾朝晖.正交对称多小波构造及其图像压缩仿真研究[J].系统仿真学报,2010,22(5),1246-1250.ZENG Zhao-hui.Construction of orthogonal symmetric multi-wavelets and simulation in image compression[J].Journal ofSystem Simulation,2010,22(5),1246-1250.
[9]唐惠玲,刘志军.多小波变换在电能质量扰动检测与分类中的应用[J].江西师范大学学报(自然科学版),2009,33(2):148-152.TANG Hui-ling,LIU Zhi-jun.The application of multiwavelettransformation in power quality disturbance detetction and clas-sification[J].Journal of Jiangxi Normal University(Natural Sci-ence),2009,33(2):148-152.
[10]高太长,韩小冬,邱实,等.基于多小波变换的电场变化仪信号去噪[J].解放军理工大学学报(自然科学版),2009,10(增刊):90-94.GAO Tai-chang,HAN Xiao-dong,QIU Shi,et al.Electric-field changes meter signal de-noising based on multi-wavelettransform[J].Journal of PLA University of Science and Tech-nology(Natural Science Edition),2009,10(Supplement):90-94.
[11]农京辉,王锦莉,刘爱林,等.利用多小波的改进多层阈值对超声图像降噪[J].计算机工程与应用,2009,45(22):138-143.NONG Jing-hui,WANG Jin-li,LIU Ai-lin,et al.Ultrasoundimage de-noising using modified multilevel threshold[J].Com-puter Engineering and Applications,2009,45(22):138-143.
[12]戴庆,卢杨,栗磊.基于多小波自适应阈值的地震图像去噪方法[J].科学技术与工程,2009,9(24):7533-7536.DAI Qing,LU Yang,LI Lei.Based on many wavelelt adaptivethreshold image denoising method of earthquake[J].ScienceTechnology and Engineering,2009,9(24):7533-7536.
[13]张蕊,王学伟,王琳.基于GHM多小波的电力系统故障录波数据压缩算法[J].电测与仪表,2008,45(10):46-50.ZHANG Rui,WANG Xue-wei,WANG Lin.Compression al-gorithm of fault recording data in power system based on GHMmultiwavelet[J].Electrical Measurement&Instrumentation,2008(5),45(10):46-50.
[14]胡海平.基于广义交叉认证的多小波阈值的图像降噪[J].应用数学与计算机数学学报,2009,23(1):61-65.HU Hai-ping.A multiwavelet threshold image denoising basedon general cross-validation[J].Communication on AppliedMathematics and Computation,2009,23(1):61-65.
[15]Downie T R,Sliverman B W.The discrete multiple wavelettransform and thresholding methods[J].IEEE Transactions onSignal Processing,1998,46(9):2558-2561.
[16]Strela V,Heller P N,Topiwala P,et al.The application ofmulti-wavelet filter banks to image processing[J].IEEETransactions on Image Processing,1999,8(4):548-563.
[17]刘志刚,钱清泉.自适应阈值多小波故障暂态信号去噪方法[J].系统工程与电子技术,2004,26(7):878-880.LIU Zhi-gang,QIAN Qing-quan.Adaptive shrinkage value de-noi-sing method of fault transient signals with multiwavelets[J].Sys-tems Engineering and Electronics,2004,26(7):878-880.
[18]谢荣生,李汉杰,孙枫,等.基于多小波噪声方差阈值的信号滤波方法[J].哈尔滨工程大学学报,2002,23(2):51-54.XIE Rong-sheng,LI Han-jie,SUN Feng,et al.Filtering algo-rithm based on multiwavelet noise variance threshold[J].Jour-nal of Harbin Engineering University,2002,23(2):51-54.
[19]刘志刚,曾怡达,钱清泉.多小波在电力系统信号消噪中的应用[J].中国电机工程学报,2004,24(1):30-34.LIU Zhi-gang,ZENG Yi-da,QIAN Qing-quan.Denoising ofelectric power system signals based on different multiwavelets[J].Proceedings of the CSEE,2004,24(1):30-34.
[20]Chen G Y,Bui T D.Multiwavelets denoising using neighboringcoefficients[J].IEEE Signal Processing Letters,2003,10(7):211-214.
[21]Cai T T,Silverman B W.Incorporating information on neigh-boring coefficients into wavelet estimation[J].Indian Journalof Statistics B,2001,63(2):127-148.
[22]卢恩博,陈俊丽,黄炳.一种改进的多小波相邻系数去噪算法[J].计算机仿真,2008,25(5):321-323.LU En-bo,CHEN Jun-li,HUANG Bing.An improved multi-wavelet denoising method using neighboring coefficients[J].Computer Simulation,2008,25(5):321-323.
[23]Bui T D,Chen G.Translation-invariant denoising using multi-wavelets[J].IEEE Transactions on Signal Processing,1998,46(12):3414-3420.
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