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Vers une caractérisation de la courbe d'incertitude pour des graphes portant des signaux

Signal processing on graphs is a recent research domain that aims at generalizing classical tools in signal processing, in order to analyze signals evolving on complex domains. Such domains are represented by graphs, for which one can compute a particular matrix, called the normalized Laplacian [3]. It was shown that the eigenvalues of this Laplacian correspond to the frequencies of the Fourier domain in classical signal processing [2]. Therefore, the frequential domain is not the same for every support graph. A consequence of this is that there is no non-trivial generalization of Heisenberg’s uncertainty principle, that states that a signal cannot be localized both in the time domain and in the frequency domain. A way to generalize this principle, introduced by Agaskar & Lu in [1], consists in determining a curve that represents a lower bound on the compromise between precision in the graph domain and precision in the spectral domain. The aim of this paper is to propose a characterization of the signals achieving this curve, for a larger class of graphs than the one studied by Agaskar & Lu.

@inproceedings{PasGriMerPas2015,
  author = {Bastien Pasdeloup and Vincent Gripon and
Grégoire Mercier and Dominique Pastor},
  title = {Vers une caractérisation de la courbe
d'incertitude pour des graphes portant des signaux},
  booktitle = {Proceedings of the GRETSI conference},
  year = {2015},
}