Towards a sampling theorem for signals on arbitrary graphs
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...
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| Published in: | 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 3864 - 3868 |
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| Main Authors: | , , |
| Format: | Conference Proceeding |
| Language: | English |
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IEEE
01-05-2014
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Anis, Aamir Gadde, Akshay Ortega, Antonio |
| Author_xml | – sequence: 1 givenname: Aamir surname: Anis fullname: Anis, Aamir email: aanis@usc.edu organization: Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA – sequence: 2 givenname: Akshay surname: Gadde fullname: Gadde, Akshay email: agadde@usc.edu organization: Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA – sequence: 3 givenname: Antonio surname: Ortega fullname: Ortega, Antonio email: ortega@sipi.usc.edu organization: Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA |
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| Snippet | 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... |
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| SubjectTerms | Bandwidth Conferences Cutoff frequency Eigenvalues and eigenfunctions Graph signal processing Laplace equations sampling theorem Signal processing spectral graph theory Symmetric matrices |
| Title | Towards a sampling theorem for signals on arbitrary graphs |
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