從最佳線性不偏預測導出的混合型碎形波收縮

Abstract

無母數迴歸問題可以被建模成具混合效果的模式。在無母數的混合效 果模式中， 高 斯-馬可夫定理提供了最佳線性不偏預測(BLUP)。 因為 碎形波具有空間的適應性和 多重 解析的性質，我們採用其作為代表複 雜訊號的基底。在本文中將利用碎形波基底 ，從BLU P的觀點，提供新 的收縮方法，已有效的去除雜訊。同時收縮的參數可以經由 資料自動決 定。我們發現這個方法可以重建訊號，減少平均平方誤差，並且不增加計 算的負擔。這 些方法並且可以適用於任何的設計。 Nonparametric regression problems can be modeled as nonparmetric mixed-effects models. The Gauss-Markov theorems of nonparametric mixed-effects models suggest the best linear unbiased prediction(BLUP) (Huang and Lu,1997). Owing to the spatial adaptivity and multiresolution analysis property, wavelets can be useful basis to represent complicated signal variability. This report will generalize the perspective of BLUP on the wavelet representation. It suggests new shrinkage methods to denoise the observed signals efficiently as demonstrated in this report. Shrinkage parameters are estimated by the data automatically in speed. The resulting adaptive wavelet shrinkage methods can reconstrct signals with small average square errors without increasing the computational cost. These methods also work for arbitary designs, including the fixed dyadic designs.