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p-exponent and p-leaders, Part I: Negative pointwise regularity

Jaffard, Stéphane and Melot, Clothilde and Leonarduzzi, Roberto and Wendt, Herwig and Abry, Patrice and Roux, Stéphane G. and Torres, Maria E. p-exponent and p-leaders, Part I: Negative pointwise regularity. (2016) Physica A Statistical Mechanics and its Applications, vol. 448. pp. 300-318. ISSN 0378-4371

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Official URL: http://dx.doi.org/10.1016/j.physa.2015.12.061

Abstract

Multifractal analysis aims to characterize signals, functions, images or fields, via the fluctuations of their local regularity along time or space, hence capturing crucial features of their temporal/spatial dynamics. Multifractal analysis is becoming a standard tool in signal and image processing, and is nowadays widely used in numerous applications of different natures. Its common formulation relies on the measure of local regularity via the H\"older exponent, by nature restricted to positive values, and thus to locally bounded functions or signals. It is here proposed to base the quantification of local regularity on p-exponents, a novel local regularity measure potentially taking negative values. First, the theoretical properties of p-exponents are studied in detail. Second, wavelet-based multiscale quantities, the p-leaders, are constructed and shown to permit accurate practical estimation of p-exponents. Exploiting the potential dependence with p, it is also shown how the collection of p-exponents enriches the classification of locally singular behaviors in functions, signals or images. The present contribution is complemented by a companion article developing the p-leader based multifractal formalism associated to p-exponents.

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/S0378437115010894
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 - INPT (FRANCE)
Other partners > Université Paris Est Créteil Val de Marne - UPEC (FRANCE)
Université de Toulouse > Université Paul Sabatier-Toulouse III - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université de Toulouse I-Sciences Sociales - 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)
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Deposited By: IRIT IRIT
Deposited On:04 Apr 2017 12:27

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