A multivariate multifractal analysis of lacunary wavelet series

Stéphane Jaffard (1) , Stéphane Seuret (1) , Herwig Wendt (2, 3) , Patrice Abry (4) , Roberto Leonarduzzi (4)

1 LAMA - Laboratoire Analyse et de Mathématiques Appliquées
2 IRIT-MINDS - CoMputational imagINg anD viSion
3 CNRS - Centre National de la Recherche Scientifique
4 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

Multivariate multifractal analysis proposes to estimate the multivariate multifractal spectrum of several signals as a way to reveal the correlations between their singularity sets. Recently discovered failures of the "natural" multifractal formalism challenge its foundations, and raise questions on the information it provides. We investigate these questions by supplying some general results on the multivariate multifractal analysis of processes satisfying the large intersection property, and illustrate it on random lacunary wavelet series.

Mots clés: Fractals; Correlation; Upper bound; Wavelet analysis; Estimation; Random processes; Size measurement

Domaines: Traitement du signal et de l'image [eess.SP]

Stéphane Jaffard, Stéphane Seuret, Herwig Wendt, Patrice Abry, Roberto Leonarduzzi. A multivariate multifractal analysis of lacunary wavelet series. IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2019), Dec 2019, Guadeloupe, France. ⟨10.1109/CAMSAP45676.2019.9022481⟩. ⟨hal-03034146⟩