
Paulo Gonçalves Inria senior researcher in the project DANTE A joint team of Inria RhoneAlpes and ENS Lyon (LIP) 
Signal Processing applied to Networks  
TimeFrequency Analysis TimeScale Analysis 

Wavelets and Fractals Wavelets History by I. Daubechies 

Wavelets and Statistics  
Other applications 
Description:
Numerical studies using ideas from statistical physics, large deviations theory and functions analysis have exhibited striking scaling invariance properties for human longterm RR interval signals. These signals are extracted from electrocardiograms and represent the time intervals between two consecutive heartbeats. The scaling invariance measured on these empirical data are reminiscent of geometric fractal properties verified theoretically by certain mathematical objects (measures or functions), which are called (selfsimilar) multifractals. These numerical studies also reveal that the scaling invariance may have different forms, according to the fact that the patients have a good health or suffer from certain cardiac diseases. These observations suggest that a good understanding of multifractal properties of cardiac signals might lead to new pertinent tools for diagnosis and surveillance. However, until now, neither satisfactory physiological origin has been associated with these properties nor mathematical objects have been proposed as good models for these signals. It is fundamental for possible medical applications in the future to go beyond the previously mentioned works and achieve a deepened study of the scaling invariance structure of cardiac signals. This requires new robust algorithms for the multifractal signals processing; specifically, it seems relevant to completement the usual statistical approach with a geometric study of the scaling invariance, based on large deviations theory. Joint work with: J. Barral, M. Sorine, C. Médigue, S. Seuret et D. Chemla within the ANR project DMASC and with P. Abry and M. Doret 