Échantillonnage de signaux sur graphes via des processus déterminantaux
Abstract
We consider the problem of sampling kbandlimited graph signals, ie, linear combinations of the first k graph Fourier modes. We know that a set of k nodes embedding all kbandlimited signals always exists, thereby enabling their perfect reconstruction after sampling. Unfortunately, to exhibit such a set, one needs to partially diagonalize the graph Laplacian, which becomes prohibitive at large scale. We propose a novel strategy based on determinantal point processes that sidesteps partial diagonalisation and enables reconstruction with only O(k) samples. While doing so, we exhibit a new general algorithm to sample determinantal process, faster than the stateoftheart algorithm by an order k.
 Publication:

arXiv eprints
 Pub Date:
 April 2017
 arXiv:
 arXiv:1704.02239
 Bibcode:
 2017arXiv170402239T
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Discrete Mathematics;
 Computer Science  Machine Learning
 EPrint:
 in French