Construction of tight wavelet-like frames on graphs

schedule le mardi 04 juin 2019 de 12h00 à 13h00

Organisé par : Castillo, Fischer, Giulini, Gribkova, Levrard, Roquain, Sangnier

Intervenant : Gilles Blanchard (Université de Potsdam)
Lieu : Paris-Diderot, salle 2015

Sujet : Construction of tight wavelet-like frames on graphs

Résumé :

We construct a frame (redundant dictionary) for the space of real-valued functions defined on a neighborhood graph constructed from data points. This frame is adapted to the underlying geometrical structure (e.g. the points belong to an unknown low dimensional manifold), has finitely many elements, and these elements are localized in frequency as well as in space. This follows a general theory developed by Coulhon et al. (2012) and is similar to a construction of Hammond et al. (2011), with the key point that we construct a tight (or Parseval) frame.  We demonstrate the interest of this representation for denoising.

Joint work with Franziska Göbel and Ulrike von Luxburg