基于一种新的阈值函数的小波域信号去噪

在D.L.Donoho和I.M.Johnstone提出的小波阈值去噪方法的基础上，构造了一个新的阈值函数．与传统的软硬阈值函数相比，新阈值函数表达式简单易于计算，克服了硬阈值函数不连续的缺点，同软阈值函数一样具有连续性，而且是高阶可导的，便于进行各种数学处理，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，同时它具有软硬阈值函数不可比拟的灵活性．仿真结果表明，采用了新的阈值函数的去噪结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，还是在信噪比增益和最小均方误差意义上均优于传统的软硬阈值方法．

Signal de-noising in wavelet domain based on a new kind of thresholding function

A novel 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 soft- and hard-thresholding function. It is simple in expression and as continuous as the soft-thresholding function, and has a high order derivative which makes convenient some kinds of mathematical disposals. 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 soft- and hard-thresholding function. All these advantages make it possible to construct an adaptive denoising algorithm. Simulation results indicate that the de-noising method adopting the new thresholding function suppresses the Pseudo-Gibbs phenomena near the singularities of the signal effectively, and the numerical results also show the new method gives better MSE performance and SNR gains than DJ's hard- and soft-thresholding methods.