A bridge between geometric measure theory and signal processing: Multifractal analysis

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

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 LAMA - Laboratoire Analyse et de Mathématiques Appliquées
3 IRIT-SC - Signal et Communications
4 CNRS - Centre National de la Recherche Scientifique

We describe the main features of wavelet techniques in multifractal analysis, using wavelet bases both as a tool for analysis, and for synthesis. We focus on two promising developments: We introduce the quantile leader method, which allows to put into light nonconcave multifractal spectra; we also test recent extensions of multifractal techniques fitted to functions that are not locally bounded but only belong to an L q space (determination of the q-spectrum).

Domaines: Informatique [cs]

Patrice Abry, Stéphane Jaffard, Herwig Wendt. A bridge between geometric measure theory and signal processing: Multifractal analysis. Groechenig, Karlheinz; Lyubarskii, Yurii; Seip, Kristian. Operator-Related Function Theory and Time-Frequency Analysis : The Abel Symposium 2012 ; ISBN : 978-3-319-08556-2, 9, Springer, pp.1--56, 2015, Abel Symposia book series (ABEL), ⟨10.1007/978-3-319-08557-9_1⟩. ⟨hal-03190198⟩