一族分段n次小波阈值参数滤波器函数

采用非线性滤波方法处理图像去噪问题时，阈值参数的选取和滤波器函数的使用对去噪图像的效果影响极大。有鉴于此，文中构造了可用于非线性滤波算法的一族分段n次小波阈值参数滤波器函数，证明了求解去噪问题必须使得泛函取最小值，而小波逼近是该泛函的近似最小值，可以用来替代Donoho的软阈值滤波器，而且次数n越大，逼近效果越好：同时证明了该n次滤波器的极限是一理想低通滤波器。

A Family of Piecewise n-Degree Filter Functions of Wavelet Threshold Parameter

When images are denoised by means of nonlinear filtering algorithms, the selections of the threshold parameter and the filter function tend to have great effects on the quality of the denoised images. In order to overcome this difficulty, a family of piecewise n-degree filter functions of wavelet threshold parameter are constructed, which can be used to nonlinear filtering algorithms. It is then proved that the wavelet approximation is a near-minimizer of the functional which has to be minimized to solve the denoising problem, and that the near-minimizer can be used to substitute the soft threshold filter of Donoho. Moreover, the bigger the degree n is, the better the approximation quality is. It is finally proved that the limit of the n-degree filter is an ideal lowpass filter.