基于邻域相关性多阈值新函数寻优法的小波降噪分析
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摘要
为了更好地获取噪声影响下的原有信号,在邻域小波系数收缩的Neigh Coeff方法基础之上,提出了一种邻域相关性多阈值新函数的小波降噪方法.该方法根据小波系数之间的相关性,将邻域窗口内所有小波系数的平方和的大小划分为邻域硬阈值、邻域窗口阈值和邻域扩张阈值.将这些邻域阈值与修正的通用阈值相比较,来实现窗口尺寸的自适应调节和小波系数的保留或收缩,以此达到消噪的目的.此外新函数的收缩因子能够较好体现与被滤波噪声的相互关系,可以进一步提高消噪的精度.然后将多阈值函数与修正的全局阈值相结合,利用混沌粒子群对邻域扩张阈值参数γ和修正的全局阈值参数α进行寻优,以获取最优小波系数的重构信号.所提方法与其它阈值函数去噪方法相比,其仿真结果表明在信号信噪比、降低有用信号失真和抑制噪声等方面都有一定的提高.
In order to better obtain the original signal under the influence of noise,on the basis of a shrinkage method of neighbouring wavelet coefficient called NeighCoeff,we propose a wavelet de-noising method based on multi-threshold new function with neighborhood correlation( MNFNC). According to the correlative characteristics of wavelet coefficients,MNFNC classifies quadratic sum of all wavelet coefficients in neighborhood window as neighboring hard threshold value,neighboring window threshold value and neighboring expansion threshold value. A comparison between these neighboring threshold values and the revised universal threshold achieves adaptive adjustment of window size and retention or shrinkage of wavelet coefficients,which is designed to remove noise. In addition,we use the shrinkage factors of MNFNC,which well reflect the relationship with the filtered noise,to decrease the effect of noise. Then,in combination with revised universal threshold,MNFNC uses chaotic particle swarm optimization algorithm to find the optimal values of parametersγ and α,which come from neighboring expansion and universal thresholds,respectively,in order to reconstruct the processed optimal wavelet coefficients to the original signal. We compare our proposed method with de-noising methods of other thresholding function,and the simulation results show MNFNC can improve the signal-to-noise ration,reduce distortion of the useful signal and effectively eliminate noise.
In order to better obtain the original signal under the influence of noise,on the basis of a shrinkage method of neighbouring wavelet coefficient called NeighCoeff,we propose a wavelet de-noising method based on multi-threshold new function with neighborhood correlation( MNFNC). According to the correlative characteristics of wavelet coefficients,MNFNC classifies quadratic sum of all wavelet coefficients in neighborhood window as neighboring hard threshold value,neighboring window threshold value and neighboring expansion threshold value. A comparison between these neighboring threshold values and the revised universal threshold achieves adaptive adjustment of window size and retention or shrinkage of wavelet coefficients,which is designed to remove noise. In addition,we use the shrinkage factors of MNFNC,which well reflect the relationship with the filtered noise,to decrease the effect of noise. Then,in combination with revised universal threshold,MNFNC uses chaotic particle swarm optimization algorithm to find the optimal values of parametersγ and α,which come from neighboring expansion and universal thresholds,respectively,in order to reconstruct the processed optimal wavelet coefficients to the original signal. We compare our proposed method with de-noising methods of other thresholding function,and the simulation results show MNFNC can improve the signal-to-noise ration,reduce distortion of the useful signal and effectively eliminate noise.
引文
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[22]周燕,刘培玉,赵静,等.基于自适应惯性权重的混沌粒子群算法[J].山东大学学报(理学版),2012,47(3):27-32.Zhou Y,Liu P Y,Zhao J,et al. Chaos particle swarm optimization based on the adaptive inertia weight[J]. Journal of Shandong University:Natural Science,2012,47(3):27-32.
[2]郑思莉,桂预风,陈先桥,等.小波阈值法在机械信号降噪研究中的应用[J].机械设计与制造,2014(1):222-225.Zheng S L,Gui Y F,Chen X Q,et al. The application of mechanical signals processing in wavelet threshold denoising method[J]. MachineryDesign and Manufacture,2014(1):222-225.
[3]徐小军,王友仁.基于离散分数阶正交小波变换图像降噪新方法[J].电子学报,2014,42(2):280-287.Xu X J,Wang Y R. Novel image denoising method based on discrete fractional orthogonal wavelet transform[J]. Acta Electronica Sinica,2014,42(2):280-287.
[4]陈丽萍,杨福增,田艳娜.基于贝叶斯估计的杂交小波图像降噪新算法[J].计算机应用研究,2012,29(9):3512-3515.Chen L P,Yang F Z,Tian Y N. New image restoration algorithm based on Bayesian hybrid wavelet transform[J]. Application Research ofComputers,2014,42(2):280-287.
[5]谢俊举,温增平,李小军,等.基于小波方法分析汶川地震近断层地震动的速度脉冲特性[J].地球物理学报,2012,55(6):1963-1972.Xie J J,Wen Z P,Li X J,et al. Analysis of velocity pulses for near-fault strong motions from the Wenchuan earthquake based on wavelet meth-od[J]. Chinese Journal of Geophysics,2014,42(2):280-287.
[6]田雅男,李月,林红波,等. GNMF小波谱分离在地震勘测噪声压制中的应用[J].地球与物理学报,2015,58(12):4568-4575.Tian Y N,L Y,Lin H B,et al. Application of GNMF wavelet spectral unmixing in seismic noise suppression[J]. Chinese Journal of Geophys-ics,2015,58(12):4568-4575.
[7]李智,张根耀,王蓓,等.基于小波变换和形态学的医学图像边缘检测[J].信息技术,2015(4):84-86.Li Z,Zhang G Y,Wang B,et al. Medical image edge detection based on wavelet transform and morphology[J]. Information Technology,2015(4):84-86.
[8]王发乃,彭良玉.一种改进的医学图像边缘检测算法[J].通信技术,2012,45(2):112-114.Wang F N,Peng L Y. An improved edge detection algorithm for medical image[J]. Communication Technology,2012,45(2):112-114.
[9] Donoho D L,Johnstone I M. Ideal spatial adaption via wavelet shrinkage[J]. Biometrika,1994,81:425-455.
[10]王亚,吕新华,王海峰.一种改进的小波阈值降噪方法及Matlab实现[J].微计算机信息,2006,22(6):259-261.Wang Y,LüX H,Wang H F. An improved method of de-noising via wavelet threshold and its implementation based on Matlab[J]. Microcom-puter Information,2006,22(6):259-261.
[11]任超,沙磊,卢献健.一种改进小波阀值算法的变形监测数据滤波方法[J].武汉大学学报(信息科学版),2012,37(7):873-875.Ren C,Sha L,Lu X J. An adaptive wavelet thresholding denoising for deformation analysis[J]. Geomatics and Information Science of WuhanUniversity,2012,37(7):873-875.
[12]赵瑞珍,宋国乡,王红.小波系数阈值估计的改进模型[J].西北工业大学学报,2001,19(4):626-628.Zhao R Z,Song G X,Wang H. Better threshold estimation of wavelet coefficients for improving denoising[J]. Journal of Northwestern Poly-technical University,2001,19(4):626-628.
[13]Cai T T,Silverman B W. Incorporating information on neighboring coefficients into wavelet estimation[J]. Sankhya:The Indian Journal of Sta-tistics,Series B,2001,63(2):127-148.
[14]Chen G,Zhu W P. Signal denoising using neighboring dualtree complex wavelet coefficients[J]. Signal Processing et,2012,6(2):143-147.
[15]Qin Y,Tian L,Wang C. Power quality disturbances detection and location based on multi-wavelet and neighboring coefficient denoising[J].International Conference on Electric Utility Deregulation and Restructuring and Power Technologies,2011:424-427.
[16]Dai J. Image denoising based on combining neighboring wavelet coefficients[J]. International Congress on Image&Signal Processing,2009:1-3.
[17]薛坚,于盛林.基于邻域相关性新阈值函数的提升小波域信号降噪法[J].信息与控制,2008,37(6):665-669.Xue J,Yu S L. Lifting wavelet-domain signal denoising based on a new threshold function with neighbor dependency[J]. Information and Con-trol,2008,37(6):665-669.
[18]Barri A,Dooms A,Schelkens P. The near shift-invariance of the dual-tree complex wavelet transform re-visited[J]. Journal of MathematicalAnalysis and Applications,2013,389(2):1303-1314.
[19]Kennedy J,Eberhart R C. Particle swarm optimization[C]//Proceedings of the IEEE International Conference on Neural Networks. Piscat-away,NJ,USA; IEEE,1995:1942-1948.
[20]吴一全,纪守新.基于混沌粒子群优化的图像Contourlet阈值去噪[J].光子学报,2010,39(9):1645-1651.Wu Y Q,Ji S X. Image contourlet threshold denoising based on chaotic particle swarm optimization[J]. Acta Photonica Sinica,2010,39(9):1645-1651.
[21]谭跃.具有混沌局部搜索策略的粒子群优化算法研究[D].长沙:中南大学,2013:45-49.Tan Y. Research on particle swarm optimization with chaotic local search[D]. Changsha:Central South University,2013:45-49.
[22]周燕,刘培玉,赵静,等.基于自适应惯性权重的混沌粒子群算法[J].山东大学学报(理学版),2012,47(3):27-32.Zhou Y,Liu P Y,Zhao J,et al. Chaos particle swarm optimization based on the adaptive inertia weight[J]. Journal of Shandong University:Natural Science,2012,47(3):27-32.