基于邻域相关性新阈值函数的提升小波域信号降噪法

Lifting Wavelet-domain Signal De-noising Based on a New Threshold Function with Neighbor Dependency

在小波阈值降噪中,在研究小波系数的软硬阈值处理方法的基础是,结合提升小波变换,提出了一种改进的基于邻域相关性的新型阈值函数.首先,介绍了提升小波阈值降噪的原理,再对新阈值函数的构造进行分析,新阈值函数有效地利用了小波系数之间的相关性,在小波系数的估计计算中考虑了邻域小波系数的大小.同时,采用改进的方法来确定降噪阈值.最后,进行降噪仿真实验,采用信噪比作为评定降噪结果的标准.仿真结果表明,新阈值函数降噪方法有效抑制了在信号奇异点附近产生的伪吉布斯现象,有较好的降噪效果.

Based on the study of soft-and-hard threshold processing method of wavelet coefficients in wavelet threshold de- noising, an improved threshold function with neighbor dependency based on lifting wavelet-domain is proposed. Firstly, the principle of lifting wavelet threshold de-noising is introduced. Then the structure of the new threshold function is analysed, and the correlative characteristics of wavelet coefficients are utilized effectively in the new function. That is, the neighboring wavelet coefficients are incorporated into the estimation of wavelet coefficients. At the same time, de-noising threshold value is determined by the improved method. Finally, simulation experiment is carded out and signal-to-noise ratio （SNR） is used as the evaluation standard of the de-noising results. Simulation results indicate that the proposed de-noising method based on the new threshold function can effectively suppress the pseudo-Gibbs phenomena near the singularities of the signal and produce better de-noising results.