Signal recovery on graphs

Random versus experimentally designed sampling

Siheng Chen, Rohan Varma, Aarti Singh, Jelena Kovacevic

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publication2015 International Conference on Sampling Theory and Applications, SampTA 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages337-341
Number of pages5
ISBN (Electronic)9781467373531
DOIs
StatePublished - Jan 1 2015
Event11th International Conference on Sampling Theory and Applications, SampTA 2015 - Washington, United States
Duration: May 25 2015May 29 2015

Other

Other11th International Conference on Sampling Theory and Applications, SampTA 2015
CountryUnited States
CityWashington
Period5/25/155/29/15

Fingerprint

Random Graphs
Recovery
Sampling
Random Sampling
Graph in graph theory
Matrix Approximation
Star Graph
Sampling Strategy
Unbiased estimator
Leverage
Low Frequency
Theoretical Analysis
Rate of Convergence
Ring
Stars
Strategy
Simulation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Signal Processing
  • Statistics and Probability

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). [7148908] 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; Kovacevic, Jelena.

2015 International Conference on Sampling Theory and Applications, SampTA 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 337-341 7148908.

Research output: Chapter in Book/Report/Conference proceedingConference 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, 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 https://doi.org/10.1109/SAMPTA.2015.7148908
Chen, Siheng ; Varma, Rohan ; Singh, Aarti ; Kovacevic, Jelena. / Signal recovery on graphs : Random versus experimentally designed sampling. 2015 International Conference on Sampling Theory and Applications, SampTA 2015. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 337-341
@inproceedings{939a9ff30aa64ef3bed9716008fbcfc1,
title = "Signal recovery on graphs: Random versus experimentally designed sampling",
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.",
author = "Siheng Chen and Rohan Varma and Aarti Singh and Jelena Kovacevic",
year = "2015",
month = "1",
day = "1",
doi = "10.1109/SAMPTA.2015.7148908",
language = "English (US)",
pages = "337--341",
booktitle = "2015 International Conference on Sampling Theory and Applications, SampTA 2015",
publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

TY - GEN

T1 - Signal recovery on graphs

T2 - Random versus experimentally designed sampling

AU - Chen, Siheng

AU - Varma, Rohan

AU - Singh, Aarti

AU - Kovacevic, Jelena

PY - 2015/1/1

Y1 - 2015/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=84941055841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941055841&partnerID=8YFLogxK

U2 - 10.1109/SAMPTA.2015.7148908

DO - 10.1109/SAMPTA.2015.7148908

M3 - Conference contribution

SP - 337

EP - 341

BT - 2015 International Conference on Sampling Theory and Applications, SampTA 2015

PB - Institute of Electrical and Electronics Engineers Inc.

ER -