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Pitfall in Multifractal Analysis of Negative Regularity

Leonarduzzi, Roberto and Wendt, Herwig and Jaffard, Stéphane and Abry, Patrice Pitfall in Multifractal Analysis of Negative Regularity. (2015) In: 25eme Colloque Groupe de Recherche et d'Etudes du Traitement du Signal et des Images (GRETSI 2015), 8 September 2015 - 11 September 2015 (Lyon, France).

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Abstract

The recent introduction of p-exponents and p-leaders extends the application of wavelet leader multifractal analysis to functions or signals with negative regularity. These new quantities are defined only for functions that are locally in Lp. However, in practice, estimations from discrete data can always be computed, even if the underlying function that models the data is not in Lp. In this case, the analysis is meaningless but indistinguishable from a valid one. In this contribution, we use a very simple function model provided by deterministic wavelet cascades to study the behavior of multifractal estimates when they are computed from discrete data that is not modeled by a function in Lp, and show that the result is a spectrum with correct shape but shifted so as to exactly be in the Lp limit. We also use numerical simulations on various multifractal random processes to show that the validity of our results extends beyond the simple model that we used.

Item Type:Conference or Workshop Item (Paper)
HAL Id:hal-01511908
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 - INPT (FRANCE)
Other partners > Université Paris Est Créteil Val de Marne - UPEC (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (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)
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Deposited By: IRIT IRIT
Deposited On:24 Mar 2017 09:46

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