Generalized Legendre transform multifractal formalism for nonconcave spectrum estimation

Roberto Leonarduzzi (1) , Hugo Touchette (2) , Herwig Wendt (3, 4) , Patrice Abry (1) , Stéphane Jaffard (5)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 National Institute for Theoretical Physics (NITheP)
3 IRIT-SC - Signal et Communications
4 CNRS - Centre National de la Recherche Scientifique
5 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: Generalized ensemble; Multifractal analysis; Wavelet leaders; Nonconcave multifractal spectrum; Legendre transform

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Intelligence artificielle [cs.AI]

Roberto Leonarduzzi, Hugo Touchette, Herwig Wendt, Patrice Abry, Stéphane Jaffard. Generalized Legendre transform multifractal formalism for nonconcave spectrum estimation. IEEE Workshop on statistical signal processing (SSP 2016), Jun 2016, Palma de Mallorca, Spain. pp. 1-5. ⟨hal-01461696⟩