基于新阈值函数的小波阈值去噪算法

小波基、分解层数、阈值和阈值函数是小波阈值去噪的关键性因素.针对小波基和分解层数的确定,提出了一个算法来实现;对于传统硬、软阈值函数的局限性和阈值函数在临界阈值处不存在平滑过渡区的现象,提出了一个参数化的新阈值函数,该阈值函数具有更高阶,通过灵活调节参数使之介于硬、软阈值函数之间,且兼具硬、软阈值函数的优点,并在临界阈值内添加平滑过渡区,可在阈值处理时保留一部分有用的高频信号,较好地抑制了细节系数的过扼杀和信号振荡现象.仿真结果表明:新阈值函数提高了去噪信号的信噪比,减小了均方误差,取得了较好的去噪效果.

Wavelet threshold de-noising algorithm based on new threshold function

The wavelet basis,decomposition levels,threshold and threshold function are the key factors of wavelet threshold de-noising.An algorithm is proposed to realize the determination of wavelet basis and decomposition levels.Aiming at limitations of the traditional hard and soft threshold function and the phenomenon of no smooth transition in the critical threshold,the new parameterized threshold function is proposed.This new threshold function has higher order,with a smooth transition at a critical threshold,making it between hard and soft threshold functions through flexibly adjust parameters and possessing the advantages of both hard and soft threshold function.What's more,it could retain part of some useful high frequency signal in threshold processing and effectively suppress the stifle of detail coefficients and the phenomenon of signal oscillation.Simulation results show that new threshold function improves the SNR of signal,reduces the MSE and obtains a better de-noising effect.