基于一种新阈值函数的小波阈值去噪方法的研究

文章利用D.L.Donoho和I.M.Johnstone提出的小波阈值去噪方法,构造了一个新的阈值函数.与传统的硬、软阈值函数相比,该阈值函数克服了硬阈值函数不连续的缺点,且同软阈值函数一样具有连续性,便于进行各种数学处理;同时还克服了软阈值函数中估计小波系数与分解小波系数之间存在着恒定偏差的缺陷,它具有硬、软阈值函数不可比拟的灵活性.仿真结果表明,新的阈值函数的去噪效果有效抑制了在信号奇异点附近产生的Pseudo-Gibbs现象,无论是在视觉效果上,还是在信噪比增益上均优于传统的硬、软阈值方法.

A De-noising Algorithm of Wavelet Threshold Based on a New Wavelet Thresholding Function

In this paper, a new thresholding function is presented based on the wavelet shrinkage put forward by D.L.Donoho and I.M.Johnstone.This new thresholding function has many advantages over DJ＇s hard- and soft-thresholding function.It is simple in expression and as continuous as the soft-thresholding function. It also overcomes the shortcoming that there is an invariable dispersion between the estimated wavelet coefficients and the decomposed wavelet coefficients of the soft-thresholding method.At the same time the new thresholding function is more elastic than the hard- and soft-thresholding functions. Simulation results indicate that the de-noising method adopting the new thresholding function suppresses the PseudoGibbs phenomena near the singularities of the signal effectively,and the numerical results also show the new method gives better SNR gains than DJ~s hard- and soft-thresholding methods.