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Finite-Resolution Effects in p-Leader Multifractal Analysis

Leonarduzzi, Roberto and Wendt, Herwig and Abry, Patrice and Jaffard, Stéphane and Melot, Clothilde Finite-Resolution Effects in p-Leader Multifractal Analysis. (2017) IEEE Transactions on Signal Processing, 65 (13). 3359-3368. ISSN 1053-587X)

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Official URL: http://doi.org/10.1109/TSP.2017.2690391

Abstract

Multifractal analysis has become a standard signal processing tool, for which a promising new formulation, the pleader multifractal formalism, has recently been proposed. It relies on novel multiscale quantities, the p-leaders, defined as local ℓ p norms of sets of wavelet coefficients located at infinitely many fine scales. Computing such infinite sums from actual finite-resolution data requires truncations to the finest available scale, which results in biased p-leaders and thus in inaccurate estimates of multifractal properties. A systematic study of such finite-resolution effects leads to conjecture an explicit and universal closed-form correction that permits an accurate estimation of scaling exponents. This conjecture is formulated from the theoretical study of a particular class of models for multifractal processes, the wavelet-based cascades. The relevance and generality of the proposed conjecture is assessed by numerical simulations conducted over a large variety of multifractal processes. Finally, the relevance of the proposed corrected estimators is demonstrated on the analysis of heart rate variability data.

Item Type:Article
Additional Information:https://ieeexplore.ieee.org/document/7891621
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 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)
Other partners > Ecole Centrale Marseille (FRANCE)
Other partners > Université de Lyon - UDL (FRANCE)
Laboratory name:
Funders:
French ANR MultiFracs under Grant ANR-16-CE33-0020
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Deposited By: IRIT IRIT
Deposited On:09 Oct 2018 14:25

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