Abstract: In order to solve the universality of threshold function in de-noising based on wavelet, a general constructing method applied to designing algorithm of wavelet threshold filtering is presented. Firstly, the aim curve of threshold function is confirmed. Secondly, a function family with different thresholds is constructed through the operation of the typical function curves satisfying the structural conditions, such as translation, rotation, scaling, and so on, and the function family approximates the objective function with different rate. Finally, the different threshold function is selected to reduce the noise according to the characteristics of the signal. Simulation and experimental results show that the characteristic of noise reduction is superior to soft and hard threshold function in SNR and MSE by this method, especially that has achieved a good balance in the sensitivity and smoothness.

Key words: de-noising based on wavelet, threshold function, constructing method

摘要： 针对小波阈值降噪方法中阈值函数的通用性问题，提出阈值函数的一般构造方法，应用于小波阈值滤波的算法设计。确定阈值函数目标曲线；通过对满足构造条件的典型函数曲线进行平移、旋转、缩放等操作，形成一个具有不同阈值，并以不同速率逼近目标函数的函数族；针对信号特点，选择不同的阈值函数进行降噪。仿真和实测信号实验表明，该方法的降噪特性在信噪比增益（SNR）和最小均方误差（MSE）上优于传统的软硬阈值函数和改进阈值函数，并在敏感度和平滑度上取得了较好的平衡。

关键词: 小波阈值降噪, 阈值函数, 构造方法