Multifractals Properties on the Near Infrared Spectroscopy of Human Brain Hemodynamic

Nonlinear physics presents us with a perplexing variety of complicated fractal objects and strange sets. Naturally one wishes to characterize the objects and describe the events occurring on them. Moreover, most time series found in “real-life” applications appear quite noisy. Therefore, at almost every point in time, they cannot be approximated either by the Taylor series or by the Fourier series of just a few terms. Many experimental time series have fractal features and display singular behavior, the so-called singularities. The multifractal spectrum quantifies the degree of fractals in the processes generating the time series. A novel definition is proposed called full-width Hölder exponents that indicate maximum expansion of multifractal spectrum. The obtained results have demonstrated the multifractal structure of near-infrared spectroscopy time series and the evidence for brain imagery activities.