Analysis of regularized LS reconstruction and random matrix ensembles in compressed sensing

Mikko Vehkapera, Yoshiyuki Kabashima, Saikat Chatterjee

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

6 Citations (Scopus)

Abstract

Performance of regularized least-squares estimation in noisy compressed sensing is studied in the limit when the problem dimensions grow large. The sensing matrix is sampled from the rotationally invariant ensemble that encloses as special cases the standard IID and row-orthogonal constructions. The analysis is carried out using the replica method in conjunction with some novel matrix integration results. The numerical experiments show that for noisy compressed sensing, the standard IID ensemble is a suboptimal choice for the measurement matrix. Orthogonal constructions provide a superior performance in all considered scenarios and are easier to implement in practice.

Original languageEnglish
Title of host publication2014 IEEE International Symposium on Information Theory, ISIT 2014
PublisherIEEE Institute of Electrical and Electronic Engineers
Pages3185-3189
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

Compressed sensing
Compressed Sensing
Random Matrices
Ensemble
Replica Method
Least Squares Estimation
Sensing
Numerical Experiment
Scenarios
Invariant
Experiments
Standards

Cite this

Vehkapera, M., Kabashima, Y., & Chatterjee, S. (2014). Analysis of regularized LS reconstruction and random matrix ensembles in compressed sensing. In 2014 IEEE International Symposium on Information Theory, ISIT 2014 (pp. 3185-3189). [6875422] IEEE Institute of Electrical and Electronic Engineers . IEEE International Symposium on Information Theory. Proceedings, Vol.. 2014 https://doi.org/10.1109/ISIT.2014.6875422
Vehkapera, Mikko ; Kabashima, Yoshiyuki ; Chatterjee, Saikat. / Analysis of regularized LS reconstruction and random matrix ensembles in compressed sensing. 2014 IEEE International Symposium on Information Theory, ISIT 2014. IEEE Institute of Electrical and Electronic Engineers , 2014. pp. 3185-3189 (IEEE International Symposium on Information Theory. Proceedings, Vol. 2014).
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Vehkapera, M, Kabashima, Y & Chatterjee, S 2014, Analysis of regularized LS reconstruction and random matrix ensembles in compressed sensing. in 2014 IEEE International Symposium on Information Theory, ISIT 2014., 6875422, IEEE Institute of Electrical and Electronic Engineers , IEEE International Symposium on Information Theory. Proceedings, vol. 2014, pp. 3185-3189, 2014 IEEE International Symposium on Information Theory, ISIT 2014, Honolulu, HI, United States, 29/06/14. https://doi.org/10.1109/ISIT.2014.6875422

Analysis of regularized LS reconstruction and random matrix ensembles in compressed sensing. / Vehkapera, Mikko; Kabashima, Yoshiyuki; Chatterjee, Saikat.

2014 IEEE International Symposium on Information Theory, ISIT 2014. IEEE Institute of Electrical and Electronic Engineers , 2014. p. 3185-3189 6875422 (IEEE International Symposium on Information Theory. Proceedings, Vol. 2014).

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

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Vehkapera M, Kabashima Y, Chatterjee S. Analysis of regularized LS reconstruction and random matrix ensembles in compressed sensing. In 2014 IEEE International Symposium on Information Theory, ISIT 2014. IEEE Institute of Electrical and Electronic Engineers . 2014. p. 3185-3189. 6875422. (IEEE International Symposium on Information Theory. Proceedings, Vol. 2014). https://doi.org/10.1109/ISIT.2014.6875422