Signal recovery on graphs: Random versus experimentally designed sampling

Siheng Chen; Rohan Varma; Aarti Singh; Jelena Kovacevic

doi:10.1109/SAMPTA.2015.7148908

Signal recovery on graphs: Random versus experimentally designed sampling

Siheng Chen, Rohan Varma, Aarti Singh, Jelena Kovacevic

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We study signal recovery on graphs based on two sampling strategies: random sampling and experimentally designed sampling. We propose a new class of smooth graph signals, called approximately bandlimited. We then propose two recovery strategies based on random sampling and experimentally designed sampling. The proposed recovery strategy based on experimentally designed sampling uses sampling scores, which is similar to the leverage scores used in the matrix approximation. We show that while both strategies are unbiased estimators for the low-frequency components, the convergence rate of experimentally designed sampling is much faster than that of random sampling when a graph is irregular¹. We validate the proposed recovery strategies on three specific graphs: a ring graph, an Erds-Rényi graph, and a star graph. The simulation results support the theoretical analysis.

Original language	English (US)
Title of host publication	2015 International Conference on Sampling Theory and Applications, SampTA 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	337-341
Number of pages	5
ISBN (Electronic)	9781467373531
DOIs	https://doi.org/10.1109/SAMPTA.2015.7148908
State	Published - Jul 2 2015
Event	11th International Conference on Sampling Theory and Applications, SampTA 2015 - Washington, United States Duration: May 25 2015 → May 29 2015

Publication series

Name	2015 International Conference on Sampling Theory and Applications, SampTA 2015

Other

Other	11th International Conference on Sampling Theory and Applications, SampTA 2015
Country/Territory	United States
City	Washington
Period	5/25/15 → 5/29/15

ASJC Scopus subject areas

Signal Processing
Statistics and Probability
Discrete Mathematics and Combinatorics

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10.1109/SAMPTA.2015.7148908

Cite this

Chen, S., Varma, R., Singh, A., & Kovacevic, J. (2015). Signal recovery on graphs: Random versus experimentally designed sampling. In 2015 International Conference on Sampling Theory and Applications, SampTA 2015 (pp. 337-341). Article 7148908 (2015 International Conference on Sampling Theory and Applications, SampTA 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SAMPTA.2015.7148908

Signal recovery on graphs: Random versus experimentally designed sampling. / Chen, Siheng; Varma, Rohan; Singh, Aarti et al.
2015 International Conference on Sampling Theory and Applications, SampTA 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 337-341 7148908 (2015 International Conference on Sampling Theory and Applications, SampTA 2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Chen, S, Varma, R, Singh, A & Kovacevic, J 2015, Signal recovery on graphs: Random versus experimentally designed sampling. in 2015 International Conference on Sampling Theory and Applications, SampTA 2015., 7148908, 2015 International Conference on Sampling Theory and Applications, SampTA 2015, Institute of Electrical and Electronics Engineers Inc., pp. 337-341, 11th International Conference on Sampling Theory and Applications, SampTA 2015, Washington, United States, 5/25/15. https://doi.org/10.1109/SAMPTA.2015.7148908

Chen S, Varma R, Singh A, Kovacevic J. Signal recovery on graphs: Random versus experimentally designed sampling. In 2015 International Conference on Sampling Theory and Applications, SampTA 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 337-341. 7148908. (2015 International Conference on Sampling Theory and Applications, SampTA 2015). doi: 10.1109/SAMPTA.2015.7148908

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abstract = "We study signal recovery on graphs based on two sampling strategies: random sampling and experimentally designed sampling. We propose a new class of smooth graph signals, called approximately bandlimited. We then propose two recovery strategies based on random sampling and experimentally designed sampling. The proposed recovery strategy based on experimentally designed sampling uses sampling scores, which is similar to the leverage scores used in the matrix approximation. We show that while both strategies are unbiased estimators for the low-frequency components, the convergence rate of experimentally designed sampling is much faster than that of random sampling when a graph is irregular1. We validate the proposed recovery strategies on three specific graphs: a ring graph, an Erds-R{\'e}nyi graph, and a star graph. The simulation results support the theoretical analysis.",

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N2 - We study signal recovery on graphs based on two sampling strategies: random sampling and experimentally designed sampling. We propose a new class of smooth graph signals, called approximately bandlimited. We then propose two recovery strategies based on random sampling and experimentally designed sampling. The proposed recovery strategy based on experimentally designed sampling uses sampling scores, which is similar to the leverage scores used in the matrix approximation. We show that while both strategies are unbiased estimators for the low-frequency components, the convergence rate of experimentally designed sampling is much faster than that of random sampling when a graph is irregular1. We validate the proposed recovery strategies on three specific graphs: a ring graph, an Erds-Rényi graph, and a star graph. The simulation results support the theoretical analysis.

AB - We study signal recovery on graphs based on two sampling strategies: random sampling and experimentally designed sampling. We propose a new class of smooth graph signals, called approximately bandlimited. We then propose two recovery strategies based on random sampling and experimentally designed sampling. The proposed recovery strategy based on experimentally designed sampling uses sampling scores, which is similar to the leverage scores used in the matrix approximation. We show that while both strategies are unbiased estimators for the low-frequency components, the convergence rate of experimentally designed sampling is much faster than that of random sampling when a graph is irregular1. We validate the proposed recovery strategies on three specific graphs: a ring graph, an Erds-Rényi graph, and a star graph. The simulation results support the theoretical analysis.

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Signal recovery on graphs: Random versus experimentally designed sampling

Abstract

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