Stochastic discrete scale invariance: Renormalization group operators and Iterated Function Systems

Pierre-Olivier Amblard (1) , Pierre Borgnat (2)

1 LIS - Laboratoire des images et des signaux
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

We revisit here the notion of discrete scale invariance. Initially defined for signal indexed by the positive reals, we present a generalized version of discrete scale invariant signals relying on a renormalization group approach. In this view, the signals are seen as fixed point of a renormalization operator acting on a space of signal. We recall how to show that these fixed point present discrete scale invariance. As an illustration we use the random iterated function system as generators of random processes of the interval that are dicretely scale invariant.

Mots clés: Discrete scale invariance; Renormalization Group operator; Iterated Function System

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

Pierre-Olivier Amblard, Pierre Borgnat. Stochastic discrete scale invariance: Renormalization group operators and Iterated Function Systems. IMA Conference on Mathematics in Signal Processing V, IMA, Dec 2004, Cirencester, United Kingdom. ⟨ensl-00175964⟩