Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals

Myung Cho; Jian Feng Cai; Suhui Liu; Yonina C. Eldar; Weiyu Xu

doi:10.1109/ICASSP.2016.7472556

Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals

Myung Cho, Jian Feng Cai, Suhui Liu, Yonina C. Eldar, Weiyu Xu

Department of Mathematics

Research output: Chapter in Book/Conference Proceeding/Report › Conference Paper published in a book › peer-review

20 Citations (Scopus)

Abstract

We propose fast algorithms that speed up or improve the performance of recovering spectrally sparse signals from un-derdetermined measurements. Our algorithms are based on a non-convex approach of using alternating projected gradient descent for structured matrix recovery. We apply this approach to two formulations of structured matrix recovery: Hankel and Toeplitz mosaic structured matrix, and Hankel structured matrix. Our methods provide better recovery performance, and faster signal recovery than existing algorithms, including atomic norm minimization.

Original language	English
Title of host publication	2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4638-4642
Number of pages	5
ISBN (Electronic)	9781479999880
DOIs	https://doi.org/10.1109/ICASSP.2016.7472556
Publication status	Published - 18 May 2016
Event	41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China Duration: 20 Mar 2016 → 25 Mar 2016

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume	2016-May
ISSN (Print)	1520-6149

Conference

Conference	41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Country/Territory	China
City	Shanghai
Period	20/03/16 → 25/03/16

Bibliographical note

Publisher Copyright:
© 2016 IEEE.

Keywords

atomic norm
compressed sensing
matrix completion
sparse recovery
spectral estimation

Access to Document

10.1109/ICASSP.2016.7472556

Cite this

Cho, M., Cai, J. F., Liu, S., Eldar, Y. C., & Xu, W. (2016). Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings (pp. 4638-4642). Article 7472556 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2016-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2016.7472556

Cho, Myung ; Cai, Jian Feng ; Liu, Suhui et al. / Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals. 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 4638-4642 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

@inproceedings{056dcde104ae4264be70b552fe2e7f4d,

title = "Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals",

abstract = "We propose fast algorithms that speed up or improve the performance of recovering spectrally sparse signals from un-derdetermined measurements. Our algorithms are based on a non-convex approach of using alternating projected gradient descent for structured matrix recovery. We apply this approach to two formulations of structured matrix recovery: Hankel and Toeplitz mosaic structured matrix, and Hankel structured matrix. Our methods provide better recovery performance, and faster signal recovery than existing algorithms, including atomic norm minimization.",

keywords = "atomic norm, compressed sensing, matrix completion, sparse recovery, spectral estimation",

author = "Myung Cho and Cai, \{Jian Feng\} and Suhui Liu and Eldar, \{Yonina C.\} and Weiyu Xu",

note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 ; Conference date: 20-03-2016 Through 25-03-2016",

year = "2016",

month = may,

day = "18",

doi = "10.1109/ICASSP.2016.7472556",

language = "English",

series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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booktitle = "2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings",

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Cho, M, Cai, JF, Liu, S, Eldar, YC & Xu, W 2016, Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals. in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings., 7472556, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. 2016-May, Institute of Electrical and Electronics Engineers Inc., pp. 4638-4642, 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016, Shanghai, China, 20/03/16. https://doi.org/10.1109/ICASSP.2016.7472556

Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals. / Cho, Myung; Cai, Jian Feng; Liu, Suhui et al.
2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2016. p. 4638-4642 7472556 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2016-May).

Research output: Chapter in Book/Conference Proceeding/Report › Conference Paper published in a book › peer-review

TY - GEN

T1 - Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals

AU - Cho, Myung

AU - Cai, Jian Feng

AU - Liu, Suhui

AU - Eldar, Yonina C.

AU - Xu, Weiyu

PY - 2016/5/18

Y1 - 2016/5/18

N2 - We propose fast algorithms that speed up or improve the performance of recovering spectrally sparse signals from un-derdetermined measurements. Our algorithms are based on a non-convex approach of using alternating projected gradient descent for structured matrix recovery. We apply this approach to two formulations of structured matrix recovery: Hankel and Toeplitz mosaic structured matrix, and Hankel structured matrix. Our methods provide better recovery performance, and faster signal recovery than existing algorithms, including atomic norm minimization.

AB - We propose fast algorithms that speed up or improve the performance of recovering spectrally sparse signals from un-derdetermined measurements. Our algorithms are based on a non-convex approach of using alternating projected gradient descent for structured matrix recovery. We apply this approach to two formulations of structured matrix recovery: Hankel and Toeplitz mosaic structured matrix, and Hankel structured matrix. Our methods provide better recovery performance, and faster signal recovery than existing algorithms, including atomic norm minimization.

KW - atomic norm

KW - compressed sensing

KW - matrix completion

KW - sparse recovery

KW - spectral estimation

UR - https://openalex.org/W2400274630

UR - https://www.scopus.com/pages/publications/84973390724

U2 - 10.1109/ICASSP.2016.7472556

DO - 10.1109/ICASSP.2016.7472556

M3 - Conference Paper published in a book

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - 4638

EP - 4642

BT - 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016

Y2 - 20 March 2016 through 25 March 2016

ER -

Cho M, Cai JF, Liu S, Eldar YC, Xu W. Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2016. p. 4638-4642. 7472556. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2016.7472556

Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals

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