Title:
   Multifractal analysis: A mathematical tool for signal classification

Abstract.
Multifractal analysis uses  families of parameters that allow to classify
signals or images.  These parameters are  based on  function spaces
regularity indices; initially the spaces used were Sobolev or
Besov spaces. New scales have recently been shown to be more relevant
for that purpose. They are defined by conditions on the walelet
decomposition of the signal.  We will describe  properties of these
``oscillation spaces''. Applications  will focus on the study of fully
developed turbulence: Statistical tests based on these criteria allow to
discriminate between several classical turbulence models which, up to
now, could not be  retained or discarded on the basis of physics
criteria. Applications to other types of signals or images will also be
presented.