基于小波阈值去噪方法的一种改进方案

利用Donoho D．L．和Johnstone I．M．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，其具有不可比拟的灵活性。该阈值函数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，便于进行各种数学处理；同时还克服了软阅值函数中小波系数估计值与分解小波系数间存在恒定偏差的缺陷。仿真结果表明，新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，无论在视觉效果，还是在信噪比增益方面均优于传统的硬、软阈值方法。

Modified Project Based on Wavelet Threshold Denoising Method

A new thresholding function was presented based on the wavelet shrinkage put forward by Donoho D. L. and Johnstone I. M. This new function has many advantages over DJ＇S hard-thresholding function and sofi-thresholding function. It is simple in expression and as continuous as the sofi-thresholding function. It also overcomes an invariable dispersion of the soft-thresholding method between the estimated wavelet coefficients and the decomposed wavelet coefficients. At the same time, the new thresholding function is more elastic than the hard-thresholding function or soft-thresholding function. Simulation results indicated that the denoising method adopting the new thresholding function suppressed the Pseudo-Gibbs phenomena near the singularities of the signal effectively, and the numerical results also showed the new method gave better SNR gains than DJ＇s hard-thresholding or soft-thresholding methods.