Stationary signal processing on graphs

Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over graphs or networks. In this paper, we generalize the traditional concept of wide sense stationarity to signals defined over the vertices of arbitrary weighted undirected graphs. We show that stationarity is intimately linked to statistical invariance under a localization operator reminiscent of translation. We prove that stationary graph signals are characterized by a well-defined Power Spectral Density that can be efficiently estimated even for large graphs. We leverage this new concept to derive Wiener-type estimation procedures of noisy and partially observed signals and illustrate the performance of this new model for denoising and regression.


Published in:
IEEE Transactions on Signal Processing, 65, 13, 3462-3477
Year:
2017
Publisher:
Piscataway, Institute of Electrical and Electronics Engineers
ISSN:
1053-587X
Keywords:
Laboratories:




 Record created 2016-01-09, last modified 2018-12-03

Preprint:
Download fulltextPDF
External links:
Download fulltextURL
Download fulltextURL
Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)