Parallel proximal methods for total variation minimization

Ulugbek S. Kamilov

doi:10.1109/ICASSP.2016.7472568

Parallel proximal methods for total variation minimization

Ulugbek S. Kamilov

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

5 Scopus citations

Abstract

Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our method replaces the standard proximal step of TV by a simpler alternative that computes several independent proximals. We prove that the proposed parallel proximal method converges to the TV solution, while requiring no sub-iterations. The results in this paper could enhance the applicability of TV for solving very large scale imaging inverse problems.

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	4697-4701
Number of pages	5
ISBN (Electronic)	9781479999880
DOIs	https://doi.org/10.1109/ICASSP.2016.7472568
State	Published - May 18 2016
Event	41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China Duration: Mar 20 2016 → Mar 25 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	03/20/16 → 03/25/16

Keywords

convex optimization
inverse problems
Proximal gradient method
total variation regularization

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10.1109/ICASSP.2016.7472568

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Kamilov, U. S. (2016). Parallel proximal methods for total variation minimization. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings (pp. 4697-4701). Article 7472568 (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.2016.7472568

@inproceedings{002c307b312b448eae8fbf2a556aeff0,

title = "Parallel proximal methods for total variation minimization",

abstract = "Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our method replaces the standard proximal step of TV by a simpler alternative that computes several independent proximals. We prove that the proposed parallel proximal method converges to the TV solution, while requiring no sub-iterations. The results in this paper could enhance the applicability of TV for solving very large scale imaging inverse problems.",

keywords = "convex optimization, inverse problems, Proximal gradient method, total variation regularization",

author = "Kamilov, \{Ulugbek S.\}",

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.2016.7472568",

language = "English",

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

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

pages = "4697--4701",

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

}

Kamilov, US 2016, Parallel proximal methods for total variation minimization. in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings., 7472568, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. 2016-May, Institute of Electrical and Electronics Engineers Inc., pp. 4697-4701, 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016, Shanghai, China, 03/20/16. https://doi.org/10.1109/ICASSP.2016.7472568

Parallel proximal methods for total variation minimization. / Kamilov, Ulugbek S.
2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2016. p. 4697-4701 7472568 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2016-May).

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

TY - GEN

T1 - Parallel proximal methods for total variation minimization

AU - Kamilov, Ulugbek S.

PY - 2016/5/18

Y1 - 2016/5/18

N2 - Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our method replaces the standard proximal step of TV by a simpler alternative that computes several independent proximals. We prove that the proposed parallel proximal method converges to the TV solution, while requiring no sub-iterations. The results in this paper could enhance the applicability of TV for solving very large scale imaging inverse problems.

AB - Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our method replaces the standard proximal step of TV by a simpler alternative that computes several independent proximals. We prove that the proposed parallel proximal method converges to the TV solution, while requiring no sub-iterations. The results in this paper could enhance the applicability of TV for solving very large scale imaging inverse problems.

KW - convex optimization

KW - inverse problems

KW - Proximal gradient method

KW - total variation regularization

UR - https://www.scopus.com/pages/publications/84973333416

U2 - 10.1109/ICASSP.2016.7472568

DO - 10.1109/ICASSP.2016.7472568

M3 - Conference contribution

AN - SCOPUS:84973333416

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

SP - 4697

EP - 4701

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 -

Kamilov US. Parallel proximal methods for total variation minimization. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2016. p. 4697-4701. 7472568. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2016.7472568

Parallel proximal methods for total variation minimization

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