Signal recovery using expectation consistent approximation for linear observations

Yoshiyuki Kabashima, Mikko Vehkaperä

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

22 Citations (Scopus)

Abstract

A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be consistent with the results obtained using the replica theory, which is supposed to be exact in the large system limit, when each entry of the observation matrix is independently generated from an identical distribution. However, this is not necessarily the case for general matrices. We show that EC recovery exhibits consistency with the replica theory for a wider class of random observation matrices. This is numerically confirmed by experiments for the Bayesian optimal signal recovery of compressed sensing using random row-orthogonal matrices.

Original languageEnglish
Title of host publication2014 IEEE International Symposium on Information Theory, ISIT 2014
PublisherIEEE Institute of Electrical and Electronic Engineers
Pages226-230
ISBN (Print)978-1-4799-5186-4
DOIs
Publication statusPublished - 1 Jan 2014
MoE publication typeA4 Article in a conference publication
Event2014 IEEE International Symposium on Information Theory, ISIT 2014 - Honolulu, HI, United States
Duration: 29 Jun 20144 Jul 2014

Publication series

SeriesIEEE International Symposium on Information Theory. Proceedings
Volume2014
ISSN2157-8095

Conference

Conference2014 IEEE International Symposium on Information Theory, ISIT 2014
CountryUnited States
CityHonolulu, HI
Period29/06/144/07/14

Fingerprint

Recovery
Replica
Approximation
Compressed sensing
Orthogonal matrix
Compressed Sensing
Mean-field Approximation
Message passing
Message Passing
Linear systems
Experiment
Observation
Experiments
Class

Cite this

Kabashima, Y., & Vehkaperä, M. (2014). Signal recovery using expectation consistent approximation for linear observations. In 2014 IEEE International Symposium on Information Theory, ISIT 2014 (pp. 226-230). [6874828] IEEE Institute of Electrical and Electronic Engineers . IEEE International Symposium on Information Theory. Proceedings, Vol.. 2014 https://doi.org/10.1109/ISIT.2014.6874828
Kabashima, Yoshiyuki ; Vehkaperä, Mikko. / Signal recovery using expectation consistent approximation for linear observations. 2014 IEEE International Symposium on Information Theory, ISIT 2014. IEEE Institute of Electrical and Electronic Engineers , 2014. pp. 226-230 (IEEE International Symposium on Information Theory. Proceedings, Vol. 2014).
@inproceedings{db82b1836054409a963a4578f62cd3a0,
title = "Signal recovery using expectation consistent approximation for linear observations",
abstract = "A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be consistent with the results obtained using the replica theory, which is supposed to be exact in the large system limit, when each entry of the observation matrix is independently generated from an identical distribution. However, this is not necessarily the case for general matrices. We show that EC recovery exhibits consistency with the replica theory for a wider class of random observation matrices. This is numerically confirmed by experiments for the Bayesian optimal signal recovery of compressed sensing using random row-orthogonal matrices.",
author = "Yoshiyuki Kabashima and Mikko Vehkaper{\"a}",
year = "2014",
month = "1",
day = "1",
doi = "10.1109/ISIT.2014.6874828",
language = "English",
isbn = "978-1-4799-5186-4",
series = "IEEE International Symposium on Information Theory. Proceedings",
publisher = "IEEE Institute of Electrical and Electronic Engineers",
pages = "226--230",
booktitle = "2014 IEEE International Symposium on Information Theory, ISIT 2014",
address = "United States",

}

Kabashima, Y & Vehkaperä, M 2014, Signal recovery using expectation consistent approximation for linear observations. in 2014 IEEE International Symposium on Information Theory, ISIT 2014., 6874828, IEEE Institute of Electrical and Electronic Engineers , IEEE International Symposium on Information Theory. Proceedings, vol. 2014, pp. 226-230, 2014 IEEE International Symposium on Information Theory, ISIT 2014, Honolulu, HI, United States, 29/06/14. https://doi.org/10.1109/ISIT.2014.6874828

Signal recovery using expectation consistent approximation for linear observations. / Kabashima, Yoshiyuki; Vehkaperä, Mikko.

2014 IEEE International Symposium on Information Theory, ISIT 2014. IEEE Institute of Electrical and Electronic Engineers , 2014. p. 226-230 6874828 (IEEE International Symposium on Information Theory. Proceedings, Vol. 2014).

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

TY - GEN

T1 - Signal recovery using expectation consistent approximation for linear observations

AU - Kabashima, Yoshiyuki

AU - Vehkaperä, Mikko

PY - 2014/1/1

Y1 - 2014/1/1

N2 - A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be consistent with the results obtained using the replica theory, which is supposed to be exact in the large system limit, when each entry of the observation matrix is independently generated from an identical distribution. However, this is not necessarily the case for general matrices. We show that EC recovery exhibits consistency with the replica theory for a wider class of random observation matrices. This is numerically confirmed by experiments for the Bayesian optimal signal recovery of compressed sensing using random row-orthogonal matrices.

AB - A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be consistent with the results obtained using the replica theory, which is supposed to be exact in the large system limit, when each entry of the observation matrix is independently generated from an identical distribution. However, this is not necessarily the case for general matrices. We show that EC recovery exhibits consistency with the replica theory for a wider class of random observation matrices. This is numerically confirmed by experiments for the Bayesian optimal signal recovery of compressed sensing using random row-orthogonal matrices.

UR - http://www.scopus.com/inward/record.url?scp=84906536415&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2014.6874828

DO - 10.1109/ISIT.2014.6874828

M3 - Conference article in proceedings

AN - SCOPUS:84906536415

SN - 978-1-4799-5186-4

T3 - IEEE International Symposium on Information Theory. Proceedings

SP - 226

EP - 230

BT - 2014 IEEE International Symposium on Information Theory, ISIT 2014

PB - IEEE Institute of Electrical and Electronic Engineers

ER -

Kabashima Y, Vehkaperä M. Signal recovery using expectation consistent approximation for linear observations. In 2014 IEEE International Symposium on Information Theory, ISIT 2014. IEEE Institute of Electrical and Electronic Engineers . 2014. p. 226-230. 6874828. (IEEE International Symposium on Information Theory. Proceedings, Vol. 2014). https://doi.org/10.1109/ISIT.2014.6874828