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Mathematical Problems in Engineering
Volume 2012, Article ID 670761, 12 pages
Research Article

Multifractals Properties on the Near Infrared Spectroscopy of Human Brain Hemodynamic

Biomedical Engineering Department, International University of Vietnam National Universities, Block 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam

Received 7 October 2011; Accepted 4 December 2011

Academic Editor: Carlo Cattani

Copyright © 2012 Truong Quang Dang Khoa and Vo Van Toi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.