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Generalized Legendre transform multifractal formalism for nonconcave spectrum estimation

Leonarduzzi, Roberto and Touchette, Hugo and Wendt, Herwig and Abry, Patrice and Jaffard, Stéphane Generalized Legendre transform multifractal formalism for nonconcave spectrum estimation. (2016) In: IEEE Workshop on statistical signal processing (SSP 2016), 26 June 2016 - 29 June 2016 (Palma de Mallorca, Spain).

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Official URL: http://dx.doi.org/10.1109/SSP.2016.7551763

Abstract

Despite widespread adoption of multifractal analysis as a signal processing tool, most practical multifractal formalisms suffer from a major drawback: since they are based on Legendre transforms, they can only yield concave estimates for multifractal spectrum that are, in most cases, only upper bounds on the (possibly nonconcave) true spectrum. Inspired by ideas borrowed from statistical physics, a procedure is devised for the estimation of not a priori concave spectra that retains the simple and efficient Legendre transform formalism structure. The potential and interest of the proposed procedure are illustrated and assessed on realizations of a synthetic multifractal process, with theoretically known nonconcave multifractal spectrum.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org This papers appears in Proceedings of IEEE SSP 2016. Electronic ISBN: 978-1-4673-7803-1 The original PDF of the article can be found at: http://ieeexplore.ieee.org/document/7551763/ Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
HAL Id:hal-01461696
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)
Other partners > Stellenbosch University - SU (SOUTH AFRICA)
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Deposited By: IRIT IRIT
Deposited On:20 Jan 2017 15:14

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