Marc Mezard (Ecole Normale Supérieure, Paris LPTMS, Université Paris Sud, CNRS) - Jeudi 14 novembre.
Compressed sensing is a major new topic in information theory. Starting from the
observation that interesting signals can be compressed, and thus are sparse in
some representation, it aims at acquiring data directly in a compressed way, using
then computational methods to reconstruct the original signal. It opens the way to
faster, less destructive, and more effective signal acquisition, with possible applications
in many branches of science, from magnetic resonance imaging to astronomy,
tomography, or gene interaction network reconstruction.
The big challenge of compressed sensing is to be able to reconstruct faithfully the
original signal -which can involve millions of variables- using the smallest possible
number of measurements. Recent developments, using concepts and methods
developed in the last fourty years in the statistical physics of disordered systems
allow to understand the existence of reconstruction thresholds due to phase transitions,
and to design new protocols which minimize the number of measurement
where the phase transition occurs, going thus beyond standard approaches based
on convex optimization.
The talk will review the basics of compressed sensing and describe the spectacular
progress that has been made using various statistical physics ideas, from spin glass
theory to crystal nucleation.
You can also watch this video on the multimedia site ENS :savoirs.ens.fr