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p-exponent and p-leaders, Part II: Multifractal Analysis. Relations to Detrended Fluctuation Analysis

Leonarduzzi, Roberto and Wendt, Herwig and Abry, Patrice and Jaffard, Stéphane and Melot, Clothilde and Roux, Stéphane G. and Torres, Maria E. p-exponent and p-leaders, Part II: Multifractal Analysis. Relations to Detrended Fluctuation Analysis. (2015) Physica A Statistical Mechanics and its Applications, 448. 319-339. ISSN 0378-4371

(Document in English)

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Official URL: http://dx.doi.org/10.1016/j.physa.2015.12.035


Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and image processing tool and is commonly used in numerous applications of different natures. In its common formulation, it relies on the H\"older exponent as a measure of local regularity, which is by nature restricted to positive values and can hence be used for locally bounded functions only. In this contribution, it is proposed to replace the H\"older exponent with a collection of novel exponents for measuring local regularity, the p-exponents. One of the major virtues of p-exponents is that they can potentially take negative values. The corresponding wavelet-based multiscale quantities, the p-leaders, are constructed and shown to permit the definition of a new multifractal formalism, yielding an accurate practical estimation of the multifractal properties of real-world data. Moreover, theoretical and practical connections to and comparisons against another multifractal formalism, referred to as multifractal detrended fluctuation analysis, are achieved. The performance of the proposed p-leader multifractal formalism is studied and compared to previous formalisms using synthetic multifractal signals and images, illustrating its theoretical and practical benefits. The present contribution is complemented by a companion article studying in depth the theoretical properties of p-exponents and the rich classification of local singularities it permits.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at Physica A Statistical Mechanics and its Applications (ISSN 0378-4371) website : http://www.sciencedirect.com/science/article/pii/S0378437115010638
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Aix-Marseille Université - AMU (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Normale Supérieure de Lyon - ENS de Lyon (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > Université Paris Est Créteil Val de Marne - UPEC (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Université Claude Bernard-Lyon I - UCBL (FRANCE)
Other partners > Ecole Centrale Marseille (FRANCE)
Other partners > Consejo Nacional de Investigaciones Científicas y Técnicas - CONICET (ARGENTINA)
Other partners > Universidad Nacional de Entre Ríos - UNER (ARGENTINA)
Laboratory name:
Deposited On:03 Apr 2017 14:14

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