A precise computation method of Lipschitz Exponent under noisy condition

In noisy condition, the accurate measurement of Lipschitz exponent is very important for many actual applications. All the modulus maxima are utilized to estimate Lipschitz exponent in each maximum line in traditional wavelet transform modulus maxima (WTMM) method, but as the positions and wavelet coefficients are corrupted in some scales by the noise, so the performance of estimation is poor. For this proposed method, the unpolluted modulus maxima are filtrated in each maxima line, and then these modulus maxima and corresponding scales are used to obtain a pre-estimation of Lipschitz exponent. Based on the pre-estimation, different weighted operations are applied to achieve the precise estimation of Lipschitz exponent. Finally, the experimental results verify the good performance of the proposed method. Keywords-Lipschitz Exponent computation, wavelet transform modulus maxima, pre-estimation, noisy condition