新阈值函数及其小波去噪研究

小波阈值法是小波域去噪的主要方法之一,该方法通过选取合适的阈值,采用阈值函数对小波系数进行相应的非线性处理,可以在均方差意义下取得最优的去噪效果.其中,选取合适的阈值函数是该方法最基本的问题之一.文章在讨论了硬阈值函数、软阈值函数和半软阈值函数的特点及其不足的基础上,提出了一个新的阈值函数.该函数在整个小波域内连续并高阶可导,而且只需要确定一个阈值,算法相对简单.仿真结果表明,与硬、软和半软阈值方法相比,采用新的阈值函数可得到较为理想的去噪效果.

A new shrinkage function and wavelet shrinkage denoising

The WaveShrink tecdhnique is one of the major methods of denoising in the wavelet domain,which is based on the principle of shrinking wavelet coefficients towards zero to remove noise.By choosing proper threshold and appling a non-linear shrinkage rule to the wavelet coefficients,the noise in signals can be well restrained,and choosing appropriate shrinkage function in WaveShrink is one of the most basic issues,which will have great effect on denoising.In this paper,the feature and shortcoming of hard,soft and semisoft shrinkage function are discussed,and a new shrinkage function is presented,which is continuous in the whole wavelet domain and has higher-order derivatives.The new shrinkage function only needs to confirm one threshold,which makes the algorithm simpler relatively.Simulation results indicate that the effect of denoising by adopting the new shrinkage function is better.