Précédent : Références Remonter : Projet FRACTALES

Abstract

The aim of the FRACTALES group is to develop theoretical tools in the field of fractal geometry, in order to finely analyze complex signals, for purposes of modelization, prediction, and synthesis.

More precisely, the FRACTALES group is concerned with the following aspects of fractal geometry:

• multifractal theory,
• iterated functions system,
• fractionnal stable processes.

The applications are numerous. They may be divided into two parts:

• 1D signals:
  • computer network traffic analysis : we model some types of computer network traffic signals as noisy stochastic multiplicative cascades
  • financial analysis : we model financial time series as fractional stable processes,
  • speech synthesis : we model speech signals as attractors of general IFS.
• 2D signals: we have designed a multifractal approach to the problem of image analysis. Defining various measures and capacities on an image, we are able to perform robust and precise image denoising and segmentation, and image compression.

For most of these subjects, the FRACTALES group has active collaborations with other research groups in France, Europe and the U.S.A., and industrial contracts with french companies.