高级搜索

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

小波滤波方法及应用

潘泉 孟晋丽 张磊 程咏梅 张洪才

潘泉, 孟晋丽, 张磊, 程咏梅, 张洪才. 小波滤波方法及应用[J]. 电子与信息学报, 2007, 29(1): 236-242. doi: 10.3724/SP.J.1146.2005.00233
引用本文: 潘泉, 孟晋丽, 张磊, 程咏梅, 张洪才. 小波滤波方法及应用[J]. 电子与信息学报, 2007, 29(1): 236-242. doi: 10.3724/SP.J.1146.2005.00233
Pan Quan, Meng Jin-li, Zhang Lei, Cheng Yong-mei, Zhang Hong-cai. Wavelet Filtering Method and Its Application[J]. Journal of Electronics and Information Technology, 2007, 29(1): 236-242. doi: 10.3724/SP.J.1146.2005.00233
Citation: Pan Quan, Meng Jin-li, Zhang Lei, Cheng Yong-mei, Zhang Hong-cai. Wavelet Filtering Method and Its Application[J]. Journal of Electronics and Information Technology, 2007, 29(1): 236-242. doi: 10.3724/SP.J.1146.2005.00233

小波滤波方法及应用

doi: 10.3724/SP.J.1146.2005.00233
基金项目: 

教育部跨世纪优秀人才培养计划基金教技函(2001)1号和国家自然科学基金(60172037, 60372085)资助项目

Wavelet Filtering Method and Its Application

  • 摘要: 小波滤波是十年来小波分析在信号处理技术中应用的一个重要领域,与传统的滤波方法相比,具有独特的优势。该文在对目前小波滤波文献进行理解和综合的基础上,通过对小波滤波问题的描述,系统论述了小波滤波的基本原理、模型和滤波特性;对小波滤波方法进行了分类,对三类基本方法进行了分析比较;着重对小波滤波方法中的基本问题进行了阐述,并对小波滤波中存在的问题和解决问题的设想及展望给出了系统的见解。
  • [1] [1] Berkner K and Wells R O. Smoothness estimates for soft-threshold denoising via translation-invariant wavelet transforms [J].Applied and Computational Harmonic Analysis.2002, 12(1):1- [2] Chang S G, Yu B, and Vetterli M. Spatially adaptive wavelet thresholding with context modeling for image denoising [J].IEEE Trans. on Image Proc.2000, 9(9):1522- [3] Lu J, Xu Y S, and Weaver J B, et al.. Noise reduction by constrained reconstructions in the wavelet-transform domain [A]. Proc. IEEE Signal Processing Society Seventh Workshop on Multidimensional Signal Processing[C], Lake Placid, New York, Sept. 23-25, 1991: 1.91.9. [4] Mallat S and Hwang W L. Singularity detection and processing with wavelets [J].IEEE Trans. on Inform. Theory.1992, 38(2):617- [5] Xu Y S, Weaver J B, and Healy D M, et al.. Wavelet transform domain filters: A spatially selective noise filtration technique [J].IEEE Trans. on Image Proc.1994, 3(6):747- [6] Donoho D L. De-noising by soft-thresholding [J].IEEE Trans. on Inform. Theory.1995, 41(3):613- [7] Lang M, Guo H, and Odegard J E, et al.. Noise reduction using an undecimated discrete wavelet transform [J].IEEE Signal Processing Letters.1996, 3(1):10- [8] Hsung T C, Lun DP-K and Siu W-C. Denoising by singularity detection [J].IEEE Trans. on Signal Proc.1999, 47(11):3139- [9] Lu J. Signal recovery and noise reduction with wavelets [D]. Dartmouth College, Hanover, NH, 1993. [10] Lu J and Heally D M. Contrast enhancement of medical images using multiscale edge representation [J].Optical Engineering.1994, 33(7):2151- [11] Rosenfeld A. A nonlinear edge detection technique [A]. Proc. of the IEEE, 1970, 58(5): 814816. [12] Donoho D L and Johnstone I M. Adapting to unknown smoothness via wavelet shrinkage [J].J. of the Amer. Statist. Assoc.1995, 90(432):1200- [13] Jansen M. Noise reduction by wavelet thresholding [M]. Springer Verlag, Lecture notes in Statistics (161), 2001. [14] Pan Q, Zhang L, and Dai G Zh, et al.. Two denoising methods by wavelet transform [J].IEEE Trans. on Signal Proc.1999, 47(12):3401- [15] Zhang L, Bao P, and Pan Q. Threshold analysis in wavelet-based de-noising [J]. IEE Electronics Letters. 2001, 37(24): 14851486. [16] Zhang L and Bao P. Denoising by spatial correlation thresholding [J].IEEE Trans. on Circuits and Systems for Video Technology.2003, 13(6):535- [17] Zhang L and Bao P. Edge detection by scale multiplication in wavelet domain [J].Pattern Recognition Letter.2002, 23(6):1771- [18] Bao P and Zhang L. Noise reduction for magnetic resonance images via adaptive multiscale products thresholding [J].IEEE Trans. on Medical Imaging.2003, 22(9):1089- [19] Zhang L, Bao P, and Wu X L. Hybrid inter-and intra-wavelet scale image restoration [J].Pattern Recognition.2003, 36(8):1737- [20] 潘泉,张磊,张洪才等. 子波域自适应滤波算法[J]. 航空学报, 1997, 18(5): 583586. [21] 潘泉,戴冠中,张洪才等. 基于阈值决策的子波域去噪方法[J]. 电子学报, 1998, 26(1): 115117. Pan Quan, Dai Guan-zhong, and Zhang Hong-cai, et al.. A threshold selection method for hard-threshold filter algorithm. Acta Electronica Sinica, 1998, 26(1): 115117. [22] 张磊,潘泉. 一种子波域滤波算法的改进[J]. 电子学报, 1999, 27(2): 1921. Zhang Lei and Pan Quan. Improvements on an adaptive filtering algorithm in wavelet transform domain. Acta Electronica Sinica, 1999, 27(2): 1921. [23] 王博,潘泉,张洪才. 基于子波分解的信号滤波算法[J]. 电子学报, 1999, 27(11), 7174. Wang Bo, Pan Quan, and Zhang Hong-cai. Signal filtering algorithm based on the wavelet transformation. Acta Electronica Sinica, 1999, 27(11), 7174. [24] 张磊,潘泉,张洪才等. 小波域滤波阈值参数c的选取[J]. 电子学报,2001, 29(3): 400402. Zhang Lei, Pan Quan, and Zhang Hong-cai, et al.. On the determination of threshold in threshold-based de-noising by wavelet transform. Acta Electronica Sinica, 2001, 29(3): 400402. [25] Rioul O and Vetterli M. Wavelets and signal processing [J]. IEEE Signal Processing Magazine, 1991, 8(4): 1438. [26] Mallat S. A theory of multiresolution signal decomposition: The wavelet transform [J].IEEE Trans. on Pattern Anal. and Machine Intel.1989, 11(7):674- [27] Vidakovic B L and Ozoya C B. On time-dependent wavelet denoising [J].IEEE Trans. on Signal Proc.1998, 46(9):2549- [28] Carl Taswell. The what, how and why of wavelet shrinkage denoising [J].Computing in Science and Engineering.2000, 2(3):12- [29] 赵瑞珍. 小波理论及其在图像、信号处理中的算法研究[D]. [博士论文], 西安:西安电子科技大学, 2001. [30] Dragotti P L and Vetterli M. Wavelet footprints: theory, algorithms, and applications [J]. J. Amer. Statist. Assoc., 2003, 51(5): 13061323. [31] Johnstone I M and Silverman B W. Wavelet threshold estimators for data with correlated noise [J].J. Royal Statistical Society B.1997, 59(2):319- [32] Jansen M and Bultheel A. Multiple wavelet threshold estimation by generalized cross validation for data with correlated noise [J].IEEE Trans. on Image Proc.1999, 8(7):947- [33] Badulescu P and Zaciu R. Removal of mixed-noise using order statistic filter and wavelet domain Wiener filter [A]. Proceedings of the International Semiconductor Conference[C]. Sinaia Romania, 1999: 301304. [34] Coifman R R and Donoho D L. Translation-invariant de-noising [A]. Wavelets in Statistics of Lecture Notes in statistics 103[C]. New York: Springer-Verlag, 1994: 125150. [35] Arne Kovac. Wavelet thresholding for unequally spaced data [D], Ph.D. Thesis, Faculty of Science, University of Bristol, 1998. [36] Vanraes E, Jansen M, and Bultheel A. Stabilized wavelet transforms for non-equispaced data smoothing [J].Signal Processing.2002, 82(12):1979- [37] Malfait M and Roose D. Wavelet-based image denoising using a Markov random field a priori model [J].IEEE Trans.on Imgae Proc.1997, 6(4):549- [38] Shark L K and Yu C. Denoising by optimal fuzzy thresholding in wavelet domain [J].Electronics Letters.2000, 36(6):581- [39] Mihcak M, Kozintsev I, and Ramchandran K, et al.. Low- complexity image denoising based on statistical modeling of wavelet coefficients [J].IEEE Signal Processing Lett.1999, 6(12):300- [40] Pizurica A and Philips W. Estimating probability of presence of a signal of interest in multiresolution single- and multiband image denoising [J]. IEEE Trans. on Image Proc. (in press). [41] Mallat S. A theory for multiresolution signal decomposition: The wavelet representation [J].IEEE Trans. on Pattern Anal. and Machine Intel.1989, 11(7):674- [42] Liu Juan. Wavelet-based statistical modeling and image estimation [D]. Ph.D. Thesis, Dept. Electrical Engineering, University of Illinois at Urbana- Champaign, 2001. [43] Hall P, Kerkyacharian G, and Picard D. On the minimax optimality of block thresholded wavelet estimators [J]. Statistica Sinica, 1999, 9(1): 3350. [44] Moulin P, and Liu J. Analysis of multiresolution image denoising schemes using generalized-Gaussian and complexity priors [J].IEEE Trans. on Inform. Theory.1999, 45(3):909- [45] Hansen M and Yu B. Wavelet thresholding via MDL for natural images [J].IEEE Trans. on Inform. Theory.2000, 46(5):1778- [46] Slader B M, and Swami A. Analysis of multiscale products for step detection and estimation [J].IEEE Trans. on Inform. Theory.1999, 45(4):1043- [47] Sender L and Selesnick I W. Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency[J].IEEE Trans. on Signal Proc.2002, 50(11):2744- [48] Shapiro J M. Embedded image coding using zerostrees of wavelet coefficients [J].IEEE Trans. on Signal Proc.1993, 41(12):3445- [49] Banham M R and Katsaggelos A K. Spatially adaptive wavelet-based multiscale image restoration [J].IEEE Trans.on Image Proc.1996, 5(4):619- [50] Crouse M S, Nowak R D, and Baraniuk R G. Wavelet-based statistical signal processing using hidden Markov models [J]. IEEE Trans. on Signal Proc., 1998, 4(46): 886902. [51] Fan G and Xia X G. Improved hidden Markov models in the wavelet-domain [J].IEEE Trans. on Signal Proc.2001, 49(1):115- [52] Romberg J K, Choi H, and Baraniuk R G. Bayesian tree-structured image modeling using wavelet-domain hidden Markov models [J].IEEE Trans. on Image Proc.2001, 10(7):1056- [53] Pizurica A, Philips W, and Lemahieu I, et al.. A versatile wavelet domain noise filtration technique for medical imaging [J].IEEE Trans. on Medical Imaging.2003, 22(5):323- [54] Liu Juan and Moulin P. Information-theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients [J].IEEE Trans. on Image Proc.2001, 10(11):1647- [55] Portilla J, Strela V, and Wainwright M J, et al.. Adaptive wiener denoising using a Gaussian scale mixture model in the wavelet domain. Proceedings of the Eight International Conference on Images Processing. Thessaloniki, Greece, 2001, 2: 3740. [56] Bruce A G and Gao H-Y. Understanding waveShrink: variance and bias estimation [J].Biometrika.1996, 83(4):727- [57] Bruce A G and Gao H-Y. Waveshrink with firm shrinkage [J]. Statistica Sinica, 1997, 7(4): 855874. [58] Gao H-Y. Wavelet shrinkage denoising using the non- negative garrote [J].J. of Computational and Graphical Statistics.1998, 7(4):469- [59] Zhang X-P and Desai M D. Adaptive denoising based on SURE risk [J].IEEE Signal Processing Lett.1998, 5(10):265- [60] Abramovich F, Sapatinas T, and Silverman B W. Wavelet thresholding via a Bayesian approach [J].J. Royal Statistical Society B.1998, 60(3):725- [61] Vidakovic B. Nonlinear wavelet shrinkage with Bayes rules and Bayes factor [J].J. of the Amer. Statist. Assoc.1998, 93(5):173- [62] Nason G P. Wavelet shrinkage using cross-validation [J]. J. Royal Statistical Society B, 1996, 58(2): 463479. [63] Jansen M, Malfait M, and Bultheel A. Generalized cross validation for wavelet thresholding [J].Signal Processing.1997, 56(1):33- [64] Abramovich F and Benjamini Y. Thresholding of wavelet coefficients as multiple hypotheses testing Procedure [Z]. In A. Antoniadis and G. Oppenheim, editors, Wavelets and Statistics, Springer, New York, 1995: 614. [65] Chang S G, Yu B, and Vetterli M. Adaptive wavelet thresholding for image denoising and compression [J].IEEE Trans. on Image Proc.2000, 9(9):1532- [66] Cohen I, Raz S, and Malah D. Translation-invariant denoising using the minimum description length criterion [J].Signal Processing.1999, 75(3):201- [67] Downie T R, and Silverman B W. The discrete multiple wavelet transform and thresholding methods [J].IEEE Trans.on Signal Proc.1998, 46(9):2558- [68] Bui T D and Chen G. Translation-invariant denoising using multiwavelets [J].IEEE Trans. on Signal Proc.1998, 46(12):3414- [69] Felix C A Fernandes. Directional.[J].shift-insensitive, complex wavelet transforms with controllable redundancy [D]. Texas AM University, Ph.D. Thesis, Houston.2002,:- [70] Candes E. Ridgelets: theory and applications [D]. Ph.D. Thesis, Department of Statistics, Stanford University, 1998. [71] Starck J L, Candes E J, and Donoho D L. The Curvelet transform for image denoising [J].IEEE Trans. on Image Proc.2002, 11(6):670- [72] Krim H, Tucker D, and Mallat S, et al.. On denoising and best signal representation [J]. IEEE Trans. on Inform. Theory, 1999, 5(7): 22252238. [73] Claypoole R L, Baraniukm R G, and Nowark R D. Adaptive wavelet transforms via lifting [A]. Proc. IEEE Conf. on Acoustics, Speech and Signal Proc.[C], Phoenix, May 12-15, 1999, vol.3: 15131516. [74] Angelini E, Esser Y J P, and Van Heertum R, et al.. Fusion of brushlet and wavelet denoising methods for nuclear images [A]. IEEE International Symposium on Biomedical Imaging [C], Macro to Nano, April 15-18, 2004, 2: 11871191. [75] Do M N and Vetterli M. Contourlets [M]. New York, Academic Press, 2003.
  • [1] 汤萍萍, 董育宁.  小波域基于分段Hurst指数的视频流分类, 电子与信息学报. doi: 10.11999/JEIT160745
    [2] 窦慧晶, 王千龙, 张雪.  基于小波阈值去噪和共轭模糊函数的时频差联合估计算法, 电子与信息学报. doi: 10.11999/JEIT150878
    [3] 吴光文, 王昌明, 包建东, 陈勇, 胡扬坡.  基于自适应阈值函数的小波阈值去噪方法, 电子与信息学报. doi: 10.3724/SP.J.1146.2013.00798
    [4] 赵小明, 赵园美, 周筱媛, 袁胜春.  一种与显示设备相关的抗颜色混叠新方法, 电子与信息学报. doi: 10.3724/SP.J.1146.2013.00636
    [5] 尹喜珍, 肖时茂, 马成炎, 叶甜春.  一种应用于全球导航卫星系统接收机的低功耗宽带压控振荡器, 电子与信息学报. doi: 10.3724/SP.J.1146.2011.00957
    [6] 张伟斌, 冯象初, 王卫卫.  图像恢复的小波域加速Landweber迭代阈值方法, 电子与信息学报. doi: 10.3724/SP.J.1146.2010.00335
    [7] 刘国军, 冯象初, 张选德.  波原子纹理图像阈值算法, 电子与信息学报. doi: 10.3724/SP.J.1146.2008.00595
    [8] 徐耀华, 王刚, 郭英.  基于时频阈值的小波包语音增强算法, 电子与信息学报. doi: 10.3724/SP.J.1146.2006.01852
    [9] 汪沛, 王岩飞, 张冰尘, 唐禹, 麻丽香.  基于贝叶斯门限的静态小波域干涉相位图滤波, 电子与信息学报. doi: 10.3724/SP.J.1146.2006.00428
    [10] 李捷, 候秀红, 韩志杰.  基于卡尔曼滤波和小波的网络流量预测算法研究, 电子与信息学报. doi: 10.3724/SP.J.1146.2005.01005
    [11] 李军侠, 水鹏朗.  基于广义高斯最大似然估计的小波域类LMMSE滤波算法, 电子与信息学报. doi: 10.3724/SP.J.1146.2006.00531
    [12] 李军侠, 水鹏朗, 郑勇.  小波变换实现图像导向滤波, 电子与信息学报. doi: 10.3724/SP.J.1146.2006.00619
    [13] 姜东焕, 宋国乡.  基于修正小波阈值的图像变分分解, 电子与信息学报. doi: 10.3724/SP.J.1146.2005.01347
    [14] 孟晋丽, 潘泉, 张洪才.  基于相邻尺度积系数的半软阈值小波滤波, 电子与信息学报. doi: 10.3724/SP.J.1146.2005.01699
    [15] 王卫卫, 水鹏朗.  基于多项式插值的小波变换预滤波器设计, 电子与信息学报.
    [16] 赵治栋, 潘敏, 陈裕泉.  小波收缩中统一阈值函数及其偏差、方差与风险分析, 电子与信息学报.
    [17] 李泽宏, 张波, 李肇基.  短沟DMOS阈值电压模型, 电子与信息学报.
    [18] 杨晋生, 蔡靖, 丁润涛.  一种具有鲁棒性的基于小波变换的滤波方法, 电子与信息学报.
    [19] 王玲, 王卫卫, 宋国乡.  多小波图像变换的自适应预滤波, 电子与信息学报.
    [20] 王永德, 何培宇, 赵刚.  一种基于小波变换的自适应滤波新方案, 电子与信息学报.
  • 加载中
  • 计量
    • 文章访问数:  6176
    • HTML全文浏览量:  112
    • PDF下载量:  4789
    • 被引次数: 0
    出版历程
    • 收稿日期:  2005-03-08
    • 修回日期:  2006-06-14
    • 刊出日期:  2007-01-19

    目录

      /

      返回文章
      返回

      官方微信,欢迎关注