Paulo Gonçalves

Inria senior researcher in the project DANTE
A joint team of Inria Rhone-Alpes and ENS Lyon (LIP)

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Signal Processing applied to Networks
Time-Frequency Analysis
Time-Scale Analysis
Wavelets and Fractals
Wavelets History
by I. Daubechies
Description: Processes with continuous but highly irregular paths occur quite commonly in a host of applications. For cascading measures, e.g, such discontinuities convey most of the pertinent information and their relevance is widely agreed upon. More generally, various complex systems are known to produce signals in which singularities may coexist in great multitude and in a highly interwoven interplay. The local degree of Holder regularity H(t) becomes then so utterly erratic as a function of location $t that its pointwise estimation becomes completely unrealistic.
With the estimation of H(t) point by point infeasible one resorts to the "multifractal formalism" which allows to quantify how frequently a given singularity strength H(t)=h is assumed, where frequency can be measured in geometrical or probabilistic terms (as the location t is chosen randomly). Consequently, several notions of so-called multifractal spectra have been proposed to quantify this occurrence in various terms. In different directions, our work focused on:
  • Wavelet-based multifractal partition function (with Rudolf Riedi)
  • Large deviations multifractal spectrum (with J. Barral)

Wavelets and Statistics
Other applications

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