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Proceedings Paper

An uncertainty principle for functions defined on graphs
Author(s): Ameya Agaskar; Yue M. Lu
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Paper Abstract

The classical uncertainty principle provides a fundamental tradeoff in the localization of a function in the time and frequency domains. In this paper we extend this classical result to functions defined on graphs. We justify the use of the graph Laplacian's eigenbasis as a surrogate for the Fourier basis for graphs, and define the notions of "spread" in the graph and spectral domains. We then establish an analogous uncertainty principle relating the two quantities, showing the degree to which a function can be simultaneously localized in the graph and spectral domains.

Paper Details

Date Published: 27 September 2011
PDF: 11 pages
Proc. SPIE 8138, Wavelets and Sparsity XIV, 81380T (27 September 2011); doi: 10.1117/12.894359
Show Author Affiliations
Ameya Agaskar, Harvard Univ. (United States)
Yue M. Lu, Harvard Univ. (United States)

Published in SPIE Proceedings Vol. 8138:
Wavelets and Sparsity XIV
Manos Papadakis; Dimitri Van De Ville; Vivek K. Goyal, Editor(s)

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