Site de Vincent Gripon

Graph-Projected Signal Processing

In the past few years, Graph Signal Processing (GSP) has attracted a lot of interest for its aim at extending Fourier analysis to arbitrary discrete topologies described by graphs. Since it is essentially built upon analogies between classical temporal Fourier transforms and ring graphs spectrum, these extensions do not necessarily yield expected convolution and translation operators when adapted on regular multidimensional domains such as 2D grid graphs. In this paper we are interested in alternate definitions of Fourier transforms on graphs, obtained by projecting vertices to regular metric spaces on which the Fourier transform is already well defined. We compare our method with classical graph Fourier transform and demonstrate its interest for designing accurate convolutional neural networks on graph signals.

@inproceedings{GreLasDupGri2018,
  author = {Nicolas Grelier and Carlos Rosar Kos
Lassance and Elsa Dupraz and Vincent Gripon},
  title = {Graph-Projected Signal Processing},
  booktitle = {IEEE GlobalSIP},
  year = {2018},
  pages = {763--767},
}