一种基于小波变换模极大值的估计 Lipschitz指数新方法

信号的奇异点和不规则部分往往包含丰富的信息,其奇异性行为通常由Lipschitz指数(Lipschitz Exponent,LE)来刻画.Mallat和Hwang在其经典文献1]中提出采用小波变换模极大值随对数尺度变化曲线的最大斜率作为LE指数的度量.该方法已被学界广泛采用.但是,由于该计算方法只是文献1]定理4不等式等号成立时的特例,故在噪声的情况下其计算的精确性和鲁棒性往往得不到保证.本文将Mallat的方法进行了改进,将对数坐标系中在小波变换尺度范围内满足文献1]定理4的直线与小波变换模极大值(Wavelet Transform Modulus Maxima,WTMM)曲线间的面积作为估算LE的目标函数.在此基础之上研究了LE的先验知识,并给出了适于工程计算的估计算法.最后进行了对比仿真实验.实验结果证明本文的方法具有更高的精确性和鲁棒性.

A Novel Method of Measuring Lipschitz Exponent Based on Wavelet Transform Modulus Maxima

Singularities and irregular structures typically characterize the content of signals.The Lipschitz Exponent (LE) is the most popular measure of the singularity behavior of a signal.Most of the existing methods of measuring LE using wavelet transform are derived from the previous work of Mallat and Hwang,which equals LE to the maximum slope of straight lines that remain above the wavelet transform modulus maxima(WTMM) curve in the log-log plot of scale s versus WTMM.However this method is not always robust and precise especially in noise environment,because it is only the particular case of the inequation (25) in 1].In this paper we adopt a new area-based objective function.Based on it,we choice the slope of the line,which minimize the objective function,as the value of LE from all the lines satisfying the inequation (25) in 1].The results of experiment demonstrate that this method is more precise and robust.