Measurement of Lipschitz Exponent (LE) using Wavelet Transform Modulus Maxima (WTMM)

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Author(s) 
Dr.P.Venkatakrishnan,S.Sangeetha, M.Sundar 

KEYWORDS 
:Lipschitz exponent, Wavelet Transform, local regularity, singularity, slope 

ABSTRACT 
Singularity and dynamical behavior are two important aspects in signal processing that carries most of signal information. A remarkable property of the wavelet transform is its ability to characterize the local regularity of functions. In mathematics, this local regularity is often measured with Lipschitz exponents (LE). The singularity, by means of a Lipschitz exponent of a function, is measured by taking a slope of a loglog plot of scales and wavelet coefficients along modulus maxima lines of a wavelet transform [1]. At present, 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 loglog 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 equation (25) in [1]. In this paper we present the measurements of lipschitz exponent using wavelet transform with a new area based objective function. The results of experiment demonstrate that this method is more precise and robust. 

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