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Volume 27 Issue 4
Apr.  2005
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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.

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

  • Received Date: 2003-10-09
  • Rev Recd Date: 2004-03-22
  • Publish Date: 2005-04-19
  • In this paper, the uniform threshold function of waveshrink is build.Cornputationally efficient formulas for computing bias, variance and risk of uniform threshold function are derived. These formulas provide a new way of understanding how waveshrink works. On the basis of this, the relation of bias, variance and risk of uniform threshold function(u=l,2,) with threshold value and wavelet coefficients are compared. These comparisons give the performance of waveshrink in finite sample situations.
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  • 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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