一种可靠的小波去噪质量评价指标
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摘要
针对传统评价指标应用于小波去噪质量评价的局限性,提出了一种复合评价指标。将各备选参数的去噪信号的均方根误差与平滑度进行归一化操作,利用变异系数定权的方法将两种指标线性组合,所得到的新指标即为复合评价指标。该指标值越小,表明其去噪效果越好,所选参数越优。理论分析证明该指标具有明确的几何和物理意义,确定了信号细节信息和逼近信息的最佳比例;多组数据分析表明该方法所确定的最佳去噪信号效果较好,简单快速且准确率高。因此,该方法是一种可靠的小波去噪质量评价指标,可以解决小波分析中诸如分解层次、小波基函数等最优参数选择的问题,服务于工程实践。
Aiming at the limitations of existing traditional evaluations applied to wavelet de-noising quality assessment,a composite evaluation is proposed.Firstly,this method will normalize the RMSE,smoothness of every de-noising signals;secondly,the two indicators are linear combinations by the use of coefficient of variation given right;lastly,the indicators obtained is composite evaluation.The index value is smaller,then the de-noising effect is more obvious and the selected parameters are better.It has been proved that the indicators have clear geometric and physical meanings through theoretical analysis,besides the best ratio of details and approximations has been determined;on the other hand,it shows that the determined best de-noising signals have better effects,simple,fast and has high accuracy through multiple sets of data analysis.Therefore,it is a reliable wavelet de-noising quality evaluation and can solve the problems of optimal parameter selection such as decomposition levels and wavelet basis functions in wavelet analysis,which will be serviced in engineering areas.
Aiming at the limitations of existing traditional evaluations applied to wavelet de-noising quality assessment,a composite evaluation is proposed.Firstly,this method will normalize the RMSE,smoothness of every de-noising signals;secondly,the two indicators are linear combinations by the use of coefficient of variation given right;lastly,the indicators obtained is composite evaluation.The index value is smaller,then the de-noising effect is more obvious and the selected parameters are better.It has been proved that the indicators have clear geometric and physical meanings through theoretical analysis,besides the best ratio of details and approximations has been determined;on the other hand,it shows that the determined best de-noising signals have better effects,simple,fast and has high accuracy through multiple sets of data analysis.Therefore,it is a reliable wavelet de-noising quality evaluation and can solve the problems of optimal parameter selection such as decomposition levels and wavelet basis functions in wavelet analysis,which will be serviced in engineering areas.
引文
[1]Huang Shengxiang,Yin hui,Jiang Zheng.Deformation Monitoring Data Processing[M].Wuhan:Wuhan University Press,2003(黄声享,尹晖,蒋征.变形监测数据处理[M].武汉:武汉大学出版社,2003)
[2]Wang Jianbo,Wan Yuanzhong,Xu Junyi,et al.Wavelet Analysis on Data Processing of Bridge Deformation Monitoring[J].Science of Surveying and Mapping,2012,37(3):79-81
[3]Ning Jinsheng,Wang Haihong,Luo Zhicai.Applications of Wavelet Analysis in Geodesy and Its Progress[J].Geomatics and Information Science of Wuhan University,2004,29(8):659-663(宁津生,汪海洪,罗志才.小波分析在大地测量中的应用及其进展[J].武汉大学学报·信息科学版,2004,29(8):659-663)
[4]Huang Shengxiang,Liu Jingnan.A Novel Method for Reducing Noises in GPS Deformation Monitoring System[J].Acta Geodaetica et Cartographica Sinica,2002,31(2):104-107(黄声享,刘经南.GPS变形监测系统中消除噪声的一种有效方法[J].测绘学报,2002,31(2):104-107)
[5]Huang Shengxiang,Liu Jingnan,Liu Xianglin.Deformation Analysis Based on Wavelet and Its Application in Dynamic Monitoring for High-rise Buildings[J].Acta Geodaetica et Cartographica Sinica,2003,32(2):153-157(黄声享,刘经南.小波分析在高层建筑动态监测中的应用[J].测绘学报,2003,32(2):153-157)
[6]Wu Fumei,Yang Yuanxi.GPS/INS Integrated Navigation by Adaptive Filtering Based on Wavelet Threshold De-noising[J].Acta Geodaetica et Cartographica Sinica,2007,36(2):124-128(吴富梅,杨元喜.基于小波阈值消噪自适应滤波的GPS/INS组合导航[J].测绘学报,2007,36(2):124-128)
[7]Yuan Debao.Wavelet Analysis for GPS Monitoring Deformation Data and Its Application[D].Beijing:China University of Mining and Technology,2009(袁德宝.GPS变形监测数据的小波分析与应用研究[D].北京:中国矿业大学,2009)
[8]Wang Zhongyu,Xia Xintao,Zhu Jianmin.Statistical Principle and Its Application in Engineering[M].Beijing:Science Press,2005(王中宇,夏新涛,朱坚民.非统计原理及其工程应用[M].北京:科学出版社,2005)
[9]Donoho D L,Johnstone J M.Ideal Spatial Adaptation by Wavelet Shrinkage[J].Biometrika,1994,81(3):425-455
[10]Li Zongchun,Deng Yong,Zhang Guanyong,et al.Deformation Measurement of Abnormal Data in the Wavelet Transform to Determine the Best Series[J].Geomatics and Information Science of Wuhan University,2011,36(3):285-288(李宗春,邓勇,张冠勇,等.变形测量异常数据中的小波变换最佳级数的确定[J].武汉大学学报·信息科学版,2011,36(3):285-288)
[11]Tao Ke,Zhu Jianjun.A Hybrid Indicator for Determining the Best Decomposition Scale of Wavelet Denoising[J].Acta Geodaetica et Cartographica Sinica,2012,41(5):749-755(陶珂,朱建军.多指标融合的小波去噪最佳分解尺度选择方法[J].测绘学报,2012,41(5):749-755)
[12]Chen Qiang,Huang Shengxiang,Wang Wei.An Evaluation Indicator of Wavelet Denoising[J].Journal of Geomatics,2008,33(5):13-14(陈强,黄声享,王韦.小波去噪效果评价的另一指标[J].测绘信息与工程,2008,33(5):13-14)
[13]Wen Hongyan.Research on Deformation Analysis Model Based on Wavelet Transform Theory[D].Wuhan:Wuhan University,2004(文鸿雁.基于小波理论的变形分析模型研究[D].武汉:武汉大学,2004)
[14]Tao Ke,Zhu Jianjun.A Comparative Study on Validity Assessment of Wavelet De-noising[J].Journal of Geodesy and Geodynamics,2012,32(2):128-133(陶珂,朱建军.小波去噪质量评价方法的对比研究[J].大地测量与地球动力学,2012,32(2):128-133)
[15]Daubechies I.Ten Lectures on Wavelets[M].NewYork:Society for Industrial and Applied Mathematics,1992
[16]Zhang Defeng.Matlab Wavelet Analysis[M].Beijing:China Machine Press,2009(张德丰.Matlab小波分析[M].北京:机械工业出版社,2009)
[17]Sun W,Mukherjee R,Stroeve P,et al.A Multiresolution Approach for Line-Edge Roughness Detection[J].Microelectronic Engineering,2009,86(3):340-351
[18]Volker D.Rhythm and Speech Rate:A Variation Coefficient forΔC[J].Language and languageprocessing,2006(1):231-241
[19]Wang Yongdi,Xu Chengquan,Fan Qian.Integrated Application of Entropy Theory,Variation Coefficient and Fuzzy Multi-criteria Decision Making in Surveying Adjustment[J].Geotechnical Investigation&Surveying,2012(9):58-61(王永弟,许承权,范千.熵权、变异系数及模糊多准则决策在测量平差中的综合应用[J].工程勘察,2012(9):58-61)
[20]Jia Lingling.Nonparametric Estimation Method of Conditional Coefficient of Variation[D].Jinan:ShanDong University,2006(贾玲玲.条件变异系数的非参数估计方法[D].济南:山东大学,2006)
[21]Wu Yunyun,Zhu Jianjun,Zuo Tingying.Investigation on the Square Root of the Linear Combination of the Square of RMSE and Smoothness for the Vondrak Filter’s Evaluation[J].Geomatics and Information Science of Wuhan University,2012,37(10):1 212-1 214(吴芸芸,朱建军,左廷英.RMSE的平方与平滑度的线性组合的平方根作为Vondrak滤波评价标准的探讨[J].武汉大学学报·信息科学版,2012,37(10):1 212-1 214)
[22]Chen Tianhua,Han Liqun,Xing Suxia,et al.Research of De-noising Method of Heart Sound Signals Based on Wavelet Transform[J].Computer Simulation,2010,27(12):401-405(陈天华,韩力群,邢素霞等.基于小波变换的心音信号滤波方法研究[J].计算机仿真,2010,27(12):401-405)
[2]Wang Jianbo,Wan Yuanzhong,Xu Junyi,et al.Wavelet Analysis on Data Processing of Bridge Deformation Monitoring[J].Science of Surveying and Mapping,2012,37(3):79-81
[3]Ning Jinsheng,Wang Haihong,Luo Zhicai.Applications of Wavelet Analysis in Geodesy and Its Progress[J].Geomatics and Information Science of Wuhan University,2004,29(8):659-663(宁津生,汪海洪,罗志才.小波分析在大地测量中的应用及其进展[J].武汉大学学报·信息科学版,2004,29(8):659-663)
[4]Huang Shengxiang,Liu Jingnan.A Novel Method for Reducing Noises in GPS Deformation Monitoring System[J].Acta Geodaetica et Cartographica Sinica,2002,31(2):104-107(黄声享,刘经南.GPS变形监测系统中消除噪声的一种有效方法[J].测绘学报,2002,31(2):104-107)
[5]Huang Shengxiang,Liu Jingnan,Liu Xianglin.Deformation Analysis Based on Wavelet and Its Application in Dynamic Monitoring for High-rise Buildings[J].Acta Geodaetica et Cartographica Sinica,2003,32(2):153-157(黄声享,刘经南.小波分析在高层建筑动态监测中的应用[J].测绘学报,2003,32(2):153-157)
[6]Wu Fumei,Yang Yuanxi.GPS/INS Integrated Navigation by Adaptive Filtering Based on Wavelet Threshold De-noising[J].Acta Geodaetica et Cartographica Sinica,2007,36(2):124-128(吴富梅,杨元喜.基于小波阈值消噪自适应滤波的GPS/INS组合导航[J].测绘学报,2007,36(2):124-128)
[7]Yuan Debao.Wavelet Analysis for GPS Monitoring Deformation Data and Its Application[D].Beijing:China University of Mining and Technology,2009(袁德宝.GPS变形监测数据的小波分析与应用研究[D].北京:中国矿业大学,2009)
[8]Wang Zhongyu,Xia Xintao,Zhu Jianmin.Statistical Principle and Its Application in Engineering[M].Beijing:Science Press,2005(王中宇,夏新涛,朱坚民.非统计原理及其工程应用[M].北京:科学出版社,2005)
[9]Donoho D L,Johnstone J M.Ideal Spatial Adaptation by Wavelet Shrinkage[J].Biometrika,1994,81(3):425-455
[10]Li Zongchun,Deng Yong,Zhang Guanyong,et al.Deformation Measurement of Abnormal Data in the Wavelet Transform to Determine the Best Series[J].Geomatics and Information Science of Wuhan University,2011,36(3):285-288(李宗春,邓勇,张冠勇,等.变形测量异常数据中的小波变换最佳级数的确定[J].武汉大学学报·信息科学版,2011,36(3):285-288)
[11]Tao Ke,Zhu Jianjun.A Hybrid Indicator for Determining the Best Decomposition Scale of Wavelet Denoising[J].Acta Geodaetica et Cartographica Sinica,2012,41(5):749-755(陶珂,朱建军.多指标融合的小波去噪最佳分解尺度选择方法[J].测绘学报,2012,41(5):749-755)
[12]Chen Qiang,Huang Shengxiang,Wang Wei.An Evaluation Indicator of Wavelet Denoising[J].Journal of Geomatics,2008,33(5):13-14(陈强,黄声享,王韦.小波去噪效果评价的另一指标[J].测绘信息与工程,2008,33(5):13-14)
[13]Wen Hongyan.Research on Deformation Analysis Model Based on Wavelet Transform Theory[D].Wuhan:Wuhan University,2004(文鸿雁.基于小波理论的变形分析模型研究[D].武汉:武汉大学,2004)
[14]Tao Ke,Zhu Jianjun.A Comparative Study on Validity Assessment of Wavelet De-noising[J].Journal of Geodesy and Geodynamics,2012,32(2):128-133(陶珂,朱建军.小波去噪质量评价方法的对比研究[J].大地测量与地球动力学,2012,32(2):128-133)
[15]Daubechies I.Ten Lectures on Wavelets[M].NewYork:Society for Industrial and Applied Mathematics,1992
[16]Zhang Defeng.Matlab Wavelet Analysis[M].Beijing:China Machine Press,2009(张德丰.Matlab小波分析[M].北京:机械工业出版社,2009)
[17]Sun W,Mukherjee R,Stroeve P,et al.A Multiresolution Approach for Line-Edge Roughness Detection[J].Microelectronic Engineering,2009,86(3):340-351
[18]Volker D.Rhythm and Speech Rate:A Variation Coefficient forΔC[J].Language and languageprocessing,2006(1):231-241
[19]Wang Yongdi,Xu Chengquan,Fan Qian.Integrated Application of Entropy Theory,Variation Coefficient and Fuzzy Multi-criteria Decision Making in Surveying Adjustment[J].Geotechnical Investigation&Surveying,2012(9):58-61(王永弟,许承权,范千.熵权、变异系数及模糊多准则决策在测量平差中的综合应用[J].工程勘察,2012(9):58-61)
[20]Jia Lingling.Nonparametric Estimation Method of Conditional Coefficient of Variation[D].Jinan:ShanDong University,2006(贾玲玲.条件变异系数的非参数估计方法[D].济南:山东大学,2006)
[21]Wu Yunyun,Zhu Jianjun,Zuo Tingying.Investigation on the Square Root of the Linear Combination of the Square of RMSE and Smoothness for the Vondrak Filter’s Evaluation[J].Geomatics and Information Science of Wuhan University,2012,37(10):1 212-1 214(吴芸芸,朱建军,左廷英.RMSE的平方与平滑度的线性组合的平方根作为Vondrak滤波评价标准的探讨[J].武汉大学学报·信息科学版,2012,37(10):1 212-1 214)
[22]Chen Tianhua,Han Liqun,Xing Suxia,et al.Research of De-noising Method of Heart Sound Signals Based on Wavelet Transform[J].Computer Simulation,2010,27(12):401-405(陈天华,韩力群,邢素霞等.基于小波变换的心音信号滤波方法研究[J].计算机仿真,2010,27(12):401-405)