基于新阈值函数及最优尺度的小波去噪研究

在Donoho D L和Johnstone I M提出的小波阈值去噪算法的基础上，首先构造了一种新的阈值函数。与传统软、硬阈值函数相比，新阈值函数不但连续，而且高阶可导，克服了硬阈值函数不连续及软阈值函数中小波估计系数与分解系数之间存在恒定偏差的缺陷。同时，为了获得更好的去噪效果，提出了基于白噪声?字2检验确定小波最优分解尺度的方法。最后，通过数值仿真实验，证明了基于白噪声?字2检验方法的有效性;在最优分解尺度下，新阈值函数在信噪比增益和最小均方误差意义上均优于传统阈值函数。

Wavelet de-noising based on novel thresholding function and best decomposition scale

A novel thresholding function is presented firstly based on the wavelet thresholding de-noising algorithm put forward by Donoho D L and Johnstone I M.Comparing with soft- and hard-thresholding function,the new thresholding function is not only continuous,but also has a high order derivative.lt overcomes the shortcomings of conventional thresholding functions,such as discontinuous of hard-thresholding and the invariable dispersion in soft-thresholding.Second,a method to determine the best decomposition scale via white noise X2 verification is presented.At last,simulation results indicate that the above method is effective and the new thresholding function gives better MMSE performance and SNR gains than conventional thresholding function.