Towards a sampling theorem for signals on arbitrary graphs

• Published in: 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 3864 - 3868
• Main Authors: Anis, Aamir, Gadde, Akshay, Ortega, Antonio
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-05-2014
• Subjects: Bandwidth; Conferences; Cutoff frequency; Eigenvalues and eigenfunctions; Graph signal processing; Laplace equations; sampling theorem; Signal processing; spectral graph theory; Symmetric matrices
• ISSN: 1520-6149; 2379-190X
• DOI: 10.1109/ICASSP.2014.6854325

In this paper, we extend the Nyquist-Shannon theory of sampling to signals defined on arbitrary graphs. Using spectral graph theory, we establish a cut-off frequency for all bandlimited graph signals that can be perfectly reconstructed from samples on a given subset of nodes. The result is analogous to the concept of Nyquist frequency in traditional signal processing. We consider practical ways of computing this cut-off and show that it is an improvement over previous results. We also propose a greedy algorithm to search for the smallest possible sampling set that guarantees unique recovery for a signal of given bandwidth. The efficacy of these results is verified through simple examples.