Random Wavelet Series

Stochastic Analysis Seminar Series

Random wavelet series were introduced in the mid 90s as simple and flexible  models that allow to take into account observed statistics of wavelet coefficients in signal and image processing. One of their most interesting properties is that they supply random processes whose pointwise regularity jumps form point to point in a very erratic way, thus supplying examples of multifractal  processes.

Interest in such models has been renewed recently under the spur of new applications coming from widely different fields; e.g.

-in functional analysis, they allow to derive the regularity properties of ``generic'' functions in a given function space (in the sense of prevalence)

-they offer toy examples on which one can check the accuracy of numerical algorithms that allow to derive the  multifractal parameters associated with signals and images.

We will give  an overview of  these properties, and we will focus on recent  extensions whose sample paths are not locally bounded, and  offer models  for signals which share this property.


Stéphane Jaffard (UPEC)

Monday, May 20, 2013 - 15:45
to 16:45