Singularity detection in human EEG signal using wavelet leaders

•To learn the fundamental concepts about singularity and discontinuity.•To imbibe the different Wavelet transform approaches WTMM, ISWM and WL.•To understand the characteristics EEG signal with different noise environment.•To savvy the statistical data processing, determine the sensitivity and specificity values from predicted and observed LE value.•To discriminate different methods using Receiver operating characteristics curve.

A proliferation of signal processing community, the dynamic behavior and the singularity detection are key steps, because dynamics and singularities carry most of signal information. Wavelet zoom is very good at localization of singularities. The Lipschitz Exponent (LE) is the most popular measure of the singularity characteristics of a signal. The singularity, by mean of an LE of a function, is measured by taking a slope of a log-log plot of scale s versus wavelet transform modulus maxima (WTMM). In this paper, we measured the singularity using WTMM, Inter Scale Wavelet Maximum (ISWM) and Wavelet Leaders (WL) by adding white Gaussian noises to the human EEG signal. The statistical performances are assessed (Mean, Standard Deviation (SD), Skewness, SD/Mean, Number of singular points (NSP)) and compared by means of non-parametric hypothesis test (Mann–Whitney U-test). Highly significant differences have been found between WTMM, ISWM and WL using Receiver Operating Characteristics (ROC) curve. WL method provides good performance of singularity measure when the more prominent noise influenced the EEG signal. The result of experiments demonstrated that a Wavelet leader is more precise and robust.