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小波收缩中统一阈值函数及其偏差、方差与风险分析

赵治栋 潘敏 陈裕泉

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[J]. 电子与信息学报, 2005, 27(4): 536-539.
引用本文: 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[J]. 电子与信息学报, 2005, 27(4): 536-539.
Zhao Zhi-dong, Pan Min, Chen Yu-quan. Bias, Variance and Risk Analysis of Uniform Threshod Function in Wavelet Shrinkage[J]. Journal of Electronics & Information Technology, 2005, 27(4): 536-539.
Citation: Zhao Zhi-dong, Pan Min, Chen Yu-quan. Bias, Variance and Risk Analysis of Uniform Threshod Function in Wavelet Shrinkage[J]. Journal of Electronics & Information Technology, 2005, 27(4): 536-539.

小波收缩中统一阈值函数及其偏差、方差与风险分析

Bias, Variance and Risk Analysis of Uniform Threshod Function in Wavelet Shrinkage

  • 摘要: 该文建立了小波阈值消噪的统一阈值函数,推导了统一阈值函数的偏差、方差、风险的明确关系式.利用这些公式研究了参数不同时(以u=1,2,为例)统一阈值函数估计的偏差、方差、风险与阈值以及小波系数的关系,得到了小波统一阈值函数消噪估计的性能,对小波消噪在工程中应用有重要的理论指导意义.
  • Mallat S著,杨力华,戴道清等译.信号处理的小波导引.北京:机械工业出版社,2002:286-327.[2]Jansen M. Noise reduction by wavelet thresholding. Springer Verlag, Lecture Notes in Statistics, 2001: 161.[3]Taswell C. The what, how, and why of wavelet shrinkage denoising[J].Computing in Science Engineering.2000, 2(3):12-[4]Donoho D L, Johnstone I. Ideal spatial adaptation by wavelet shrinkage[J].Biometrika.1994, 81(3):425-[5]Donoho D L. De-noising by soft-thresholding. IEEE Trans. on Info. Theory, 1995, 41(3): 612 - 627.[6]Donoho D L, Johnstone I, Kerkacharian G. Wavelet shrinkage:Asymptopia? J. of the Loyal Statist. Soc. Ser. B, 1995, 57(2):301 - 369.[7]Antoniadis A. Wavelets in statistics: a review[J].J. Ital. Statist. Soc.1997, 6(1):97-[8]Abramovich F, Bailey T C, Sapatinas T. Wavelet analysis and its statistical applications[J].The Statistician-J. of the Royal Statist. Soc.Ser. D.2000, 49(1):1-[9]Bruce A G, Gao H Y. WaveShrink:shrinkage functions and thresholds[J].SPIE.1995, 2569:270-[10]Bruce A G, Gao H Y. Understanding waveshrink: variance and bias estimation[J].Biometrika.1996, 83(4):727-[11]Gao H Y. Wavelet shrinkage denoising using the non-negative garrote[J].J. Comput. Graph. Statist.1998, 7(4):469-[12]Marron J S, Adak S. Exact risk analysis of wavelet regression[J].J Comput Graph. Statist.1998, 7(3):278-[13]Jansen M. Asymptotic behavior of the minimum mean squared error threshold for noisy wavelet coefficients ofpiecewise smooth signals[J].IEEE Trans. on Signal Proc.2001, 49(6):1113-
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出版历程
  • 收稿日期:  2003-10-09
  • 修回日期:  2004-03-22
  • 刊出日期:  2005-04-19

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