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

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 in [1], 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.