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Tenets, Methods, and Applications of Multifractal Analysis in Neurosciences

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The Fractal Geometry of the Brain

Part of the book series: Springer Series in Computational Neuroscience ((NEUROSCI))

Abstract

The characteristics of biomedical signals are not captured by conventional measures like the average amplitude of the signal. The methodologies derived from fractal geometry have been a very useful approach to study the degree of irregularity of a signal. The monofractal analysis of a signal is defined by a single power-law exponent in assuming a scale invariance in time and space. However, temporal and spatial variation in scale invariant structure of the biomedical signal often appears. In this case, the multifractal analysis is well suited because it is defined by a multifractal spectrum of power-law exponents. There are several approaches to the implementation of this analysis and there are numerous ways to present these.

In this chapter, we review the use of multifractal analysis for the purpose of characterizing signals in neurosciences. After describing the tenets of multifractal analysis, we present the several approaches to the estimation of the multifractal spectrum. Finally, we describe the application of this spectrum on biomedical signals in the characterization of several diseases in neurosciences.

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Author information

Authors and Affiliations

  1. Clinical Imaging Core Facility (CI2C), INSERM U1171, Lille University Hospital, Lille, France

    Renaud Lopes

  2. CNRS 8524 UMR, Lille 1 University – Sciences and Technology, Villeneuve d’Ascq, France

    Antoine Ayache

Authors
  1. Renaud Lopes
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  2. Antoine Ayache
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Correspondence to Renaud Lopes .

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Editors and Affiliations

  1. Department of Surgery Division of Neurosurgery, University of Toronto St. Michael's Hospital, Toronto, Ontario, Canada

    Antonio Di Ieva

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Lopes, R., Ayache, A. (2016). Tenets, Methods, and Applications of Multifractal Analysis in Neurosciences. In: Di Ieva, A. (eds) The Fractal Geometry of the Brain. Springer Series in Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3995-4_4

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