小波收縮中統(tǒng)一閾值函數(shù)及其偏差、方差與風險分析

趙治棟; 潘敏; 陳裕泉

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小波收縮中統(tǒng)一閾值函數(shù)及其偏差、方差與風險分析

趙治棟, 潘敏, 陳裕泉

文章導航 > 電子與信息學報 > 2005 > 27(4): 536-539

趙治棟, 潘敏, 陳裕泉. 小波收縮中統(tǒng)一閾值函數(shù)及其偏差、方差與風險分析[J]. 電子與信息學報, 2005, 27(4): 536-539.

引用本文:

趙治棟, 潘敏, 陳裕泉. 小波收縮中統(tǒng)一閾值函數(shù)及其偏差、方差與風險分析[J]. 電子與信息學報, 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.

趙治棟, 潘敏, 陳裕泉. 小波收縮中統(tǒng)一閾值函數(shù)及其偏差、方差與風險分析[J]. 電子與信息學報, 2005, 27(4): 536-539.

引用本文:

趙治棟, 潘敏, 陳裕泉. 小波收縮中統(tǒng)一閾值函數(shù)及其偏差、方差與風險分析[J]. 電子與信息學報, 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.

小波收縮中統(tǒng)一閾值函數(shù)及其偏差、方差與風險分析

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出版歷程
- 收稿日期: 2003-10-09
- 修回日期: 2004-03-22
- 刊出日期: 2005-04-19

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

摘要

摘要: 該文建立了小波閾值消噪的統(tǒng)一閾值函數(shù),推導了統(tǒng)一閾值函數(shù)的偏差、方差、風險的明確關系式.利用這些公式研究了參數(shù)不同時(以u=1,2,為例)統(tǒng)一閾值函數(shù)估計的偏差、方差、風險與閾值以及小波系數(shù)的關系,得到了小波統(tǒng)一閾值函數(shù)消噪估計的性能,對小波消噪在工程中應用有重要的理論指導意義.
- 小波收縮; 閾值函數(shù); 偏差估計; 方差估計; 風險估計
Abstract: 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,楊力華,戴道清等譯.信號處理的小波導引.北京:機械工業(yè)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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