[en] Multifractal analysis is concerned with the study of very irregular signals. For such functions, the pointwise regularity may change widely from a point to another. Therefore, it is more interesting to determine the spectrum of singularities of the signal, which is the Hausdor ff dimension of the
set of points which have the same H ölder exponent. For real-life signals, the computation of the spectrum of singularities from its de finition is not feasible. Multifractal formalisms are used to approximate this spectrum. Currently, there exist several methods. In this talk, we present a new multifractal formalism based on the wavelet leaders of a signal which allows to detect non concave and non increasing spectra.
Disciplines :
Mathematics
Author, co-author :
Esser, Céline ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Kleyntssens, Thomas ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Bastin, Françoise ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Nicolay, Samuel ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
Detection of non concave and non increasing multifractal spectra using wavelet leaders (Part I)