An uncertainty principle for functions defined on graphs

Ameya Agaskar; Yue M. Lu

doi:10.1117/12.894359

27 September 2011 An uncertainty principle for functions defined on graphs

Ameya Agaskar, Yue M. Lu

Proceedings Volume 8138, Wavelets and Sparsity XIV; 81380T (2011) https://doi.org/10.1117/12.894359
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

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.

Citation Download Citation

Ameya Agaskar and Yue M. Lu "An uncertainty principle for functions defined on graphs", Proc. SPIE 8138, Wavelets and Sparsity XIV, 81380T (27 September 2011); https://doi.org/10.1117/12.894359

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