小波收縮中統(tǒng)一閾值函數(shù)及其偏差、方差與風(fēng)險(xiǎn)分析
Bias, Variance and Risk Analysis of Uniform Threshod Function in Wavelet Shrinkage
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摘要: 該文建立了小波閾值消噪的統(tǒng)一閾值函數(shù),推導(dǎo)了統(tǒng)一閾值函數(shù)的偏差、方差、風(fēng)險(xiǎn)的明確關(guān)系式.利用這些公式研究了參數(shù)不同時(shí)(以u(píng)=1,2,為例)統(tǒng)一閾值函數(shù)估計(jì)的偏差、方差、風(fēng)險(xiǎn)與閾值以及小波系數(shù)的關(guān)系,得到了小波統(tǒng)一閾值函數(shù)消噪估計(jì)的性能,對(duì)小波消噪在工程中應(yīng)用有重要的理論指導(dǎo)意義.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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