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Extending multifractal analysis to negative regularity: p-exponents and p-leaders

Leonarduzzi, Roberto and Wendt, Herwig and Jaffard, Stéphane and Roux, Stéphane and Torres, Maria E. and Abry, Patrice Extending multifractal analysis to negative regularity: p-exponents and p-leaders. (2014) In: IEEE International Conference on Acoustics, Speech, and Signal Processing - ICASSP 2014, 5 May 2014 - 9 May 2014 (Florence, Italy).

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Official URL: http://dx.doi.org/10.1109/ICASSP.2014.6853607


Scale invariance is a widely used concept to analyze real-world data from many different applications and multifractal analysis has become the standard corresponding signal processing tool. It characterizes data by describing globally and geometrically the fluctuations of local regularity, usually measured by means of the Hölder exponent. A major limitation of the current procedure is that it applies only to locally bounded functions or signals, i.e., to signals with positive regularity. The present contribution proposes to characterize local regularity with a new quantity, the p-exponent, that permits negative regularity in data, a widely observed property in real-world data. Relations to Hölder exponents are detailed and a corresponding p-leader multifractal formalism is devised and shown at work on synthetic multifractal processes, representative of a class of models often used in applications. We formulate a conjecture regarding the equivalence between Hölder and p-exponents for a subclass of processes. Even when Hölder and p-exponents coincide, the p-leader formalism is shown to achieve better estimation performance.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6853607
HAL Id:hal-01147322
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution: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 > Consejo Nacional de Investigaciones Científicas y Técnicas - CONICET (ARGENTINA)
Other partners > Université Paris-Est Marne-La-Vallée - UPEM (FRANCE)
Other partners > Universidad Nacional de Entre Ríos - UNER (ARGENTINA)
Laboratory name:
ANR-BLANC-2011-AMATIS-BS0101102 - CNRS-CONICET-grant-2010-112432
Deposited On:23 Apr 2015 11:04

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