传统的小波去噪算法是对含噪信号的正交小波分解系数硬取阀值或软取阀值(该文提出软取的阀值应大约为硬取阀值的一半),这种算法可能会使重构信号在奇异点邻域产生人为的振荡,即Gibbs现象。能有效消除或减弱振荡的一个有效方法是对含噪信号进行在某个范围内所有可能的循环平移(实际上反向平移小波),然后用阀值估计信号,并对逆平移后的估计取平均得到重构信号。该文研究了平均平移算法的实现及平移范围与去噪效果的关系。De-Noising with traditional wavelet transform is applying the soft or hard thresholding to the coefficients of the noisy signal transformed into an orthogonal wavelet domain(this paper proposes that the soft thresholding should be a half of the hard thresholding).It may produce artifacts on discontinuities of the signal(Gibbs phenomena).One effective method to suppress such artifacts is,for a range of shifts,one shifts the data(in practice people shift the wavelet basis),De-Noises the shifted data,and then unshifts the de-noised data.Doing this for each of a range of shifts and averaging all the results so obtain a reconstruction signal.This paper also studies the realization of averaging shift algorithm as well as the relationship between shift range and de-noising effect.国家自然科学基金(编号:79970079
