NATO Advanced Study Institute 
Topic 



Timefrequency and timescale transforms 
Lecturer 


Bruno Torresani
Centre de Physique Theorique, Marseille 
Abstract 


Current multimedia technologies call for efficient ways of representing
signals. Efficiency may be understood from several points of view,
in particular the following three:
efficiency from the point of view of signal compression, i.e.
for representing maximal amount of information within
minimal amount of data. Or efficiency from the point of
view of signal analysis, i.e. ability of providing a
representation which is simple enough so that information
may be easily retrieved. Or efficiency from algorithmic points
of view.
We shall review several methods for signal representation, which may be termed ``efficient'' from the above mentioned points of view. We shall especially focus on some representations based upon the notion of localization in timefrequency or timescale spaces. We shall pay special attention to the representations which are adapted to ``nonstationary'' features of signals, in particular the classes of bilinear representations (in particular the Wigner representations, and their generalizations), and their approximations using timefrequency atoms (mainly wavelet transforms and Gabor transforms). Among the applications of such methods, we shall more particularly emphasize concrete (and potential) applications to signal compression and signal denoising, as well as applications to detection and parameter estimation problems. 
Biography 


B. Torresani was born in Marseille, France, on November 23th, 1961.
He received his PhD degree in theoretical physics (July 1986)
from the Universite de Provence (Marseille), and his habilitation
degree (October 1993) from the Universite de la Mediterranee
(Marseille). He has been appointed Alexander von Homboldt fellow in
Bochum (FRG), and associate professor in St Louis (Missouri),
Irvine (California), LouvainlaNeuve (Belgium) and La Plata (Argentina).
He currently holds a research position at CNRS, and a joint
appointment at the Centre de Physique Theorique and the
Laboratoire d'Analyse, Topologie et Probabilites.
B. Torresani's research interests are mainly in signal analysis and timefrequency methods, numerical electromagnetic scattering, mathematical physics and computational biology. 
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