Presentation

Research interests

In my thesis, I study the pointwise irregularity of signals with the Hölder exponents. For very irregular functions, it does not make sense to try to characterize the pointwise irregularity because it can change from one point to another. It is more interesting to compute the spectrum of singularities, that is "the size" of the set of points which share the same pointwise irregularity and by size, one means the Hausdorff dimension. Further, this size must be efficiently computable. One uses therefore an indirect way to compute it, the multifractal formalism.

The first multifractal formalism was introduced by Frisch and Parisi in the context of fully developed turbulences in 1988. Several formalisms are based on this first multifractal formalism but are using the wavelets. Unfortunately, they have a drawback: they can only detect concave spectra. For this reason, Stéphane Jaffard has introduced the S^{\nu} spaces in 2004.

My research can be divided into several parts:

  • the theoritical part consists in generalising the S^{\nu} spaces to better characterise the fractal signals;
  • the practical part consists in developing and implementing algorithms to approximate spectra of singularities;
  • I also study the fractal nature of 2D-signals.

For more details, see Research.