基于SURE无偏估计的自适应小波阈值去噪

Adaptive Wavelet Thresholding Denoising method Based on SURE Estimation

本文在D .L .Dohono提出的小波阈值去噪的基础上 ,提出了一种新的阈值函数 ,与原来的分段阈值函数相比 ,此函数具有明显优点 ,表达式简单易于计算 ,连续可微 ,易于求导 .此函数的这些优点为实现信号的自适应去噪提供了可能 .本文应用此阈值函数 ,基于SURE无偏估计 ,给出了一种自适应去噪方法 .并用受污染的blocks、bumps、heavysine、doppler等典型信号做实验 ,实验结果显示此方法能在最小均方误差 (MSE)意义上收敛 。

This paper presents a novel adaptive denoising method based on wavelet shrinkage method. First, we present a new class of thresholding function that has continuous derivative while the derivative of standard soft-thresholding function is not continuous. The new thresholding function makes it possible to construct an adaptive algorithm whenever using the wavelet shrinkage method. Second, by using the new thresholding function, we present an adaptive method based on SURE Risk. At last several numerical example are given, the result shows that the proposed method is very effective in adaptively finding the optimal solution in mean square error(MSE)sense. It also indicates that this method gives better MSE performance than other wavelet shrinkage methods.