The Signal and Communication group works in the following research domains:
> Statistical signal processing for communications. The first area of our research activities concerned blind estimation techniques for radio spectrum monitoring. We pursued our works in blind source separation, concentrating more than, in the past, on digital communication applications. Finally, we significantly developed our activity on random matrices and their use in digital communications and signal processing. In particular, we generalized some existing mathematical results to more complex models in order to provide more realistic models in our applicative contexts.
> Wavelets and image processing. Different contexts of the use of wavelet representations have been considered: compression, vision (disparity estimation) and restoration. However, our efforts mainly focused on image restoration, for which variational approaches have been proposed, using recently developed convex analysis tools. In the particular case of image denoising, it appeared preferable to adopt alternative nonlinear estimation approaches based on Stein’s principle. The interest of frame analyses was also emphasized by concentrating on dual-trees and oversampled filter banks introducing a reduced redundancy.
> Information theory. Different aspects of information theory have been tackled: contributions have been brought to non-extensive statistics, introduced in statistical physics by C. Tsallis in 1988. We also studied conditions for the extension of some uncertainty inequalities such as Bialynicki-Birula's and Mycielski's ones. Finally, studies of maximal Rényi entropy laws under constraints and their interpretations constitute one of our main activities.