Generalized total variation denoising via augmented Lagrangian cycle spinning with Haar wavelets

Ulugbek Kamilov; Emrah Bostan; Michael Unser

doi:10.1109/ICASSP.2012.6288032

Generalized total variation denoising via augmented Lagrangian cycle spinning with Haar wavelets

Ulugbek Kamilov
, Emrah Bostan
, Michael Unser

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

5 Scopus citations

Abstract

We consider the denoising of signals and images using regularized least-squares method. In particular, we propose a simple minimization algorithm for regularizers that are functions of the discrete gradient. By exploiting the connection of the discrete gradient with the Haar-wavelet transform, the n-dimensional vector minimization can be decoupled into n scalar minimizations. The proposed method can efficiently solve total-variation (TV) denoising by iteratively shrinking shifted Haar-wavelet transforms. Furthermore, the decoupling naturally lends itself to extensions beyond ℓ ₁ regularizers.

Original language	English
Title of host publication	2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings
Pages	909-912
Number of pages	4
DOIs	https://doi.org/10.1109/ICASSP.2012.6288032
State	Published - 2012
Event	2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Kyoto, Japan Duration: Mar 25 2012 → Mar 30 2012

Publication series

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

Conference

Conference	2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012
Country/Territory	Japan
City	Kyoto
Period	03/25/12 → 03/30/12

Keywords

cycle spinning
signal denoising
soft-thresholding
TV denoising

Access to Document

10.1109/ICASSP.2012.6288032

Cite this

Kamilov, U., Bostan, E., & Unser, M. (2012). Generalized total variation denoising via augmented Lagrangian cycle spinning with Haar wavelets. In 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings (pp. 909-912). Article 6288032 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2012.6288032

Kamilov, Ulugbek ; Bostan, Emrah ; Unser, Michael. / Generalized total variation denoising via augmented Lagrangian cycle spinning with Haar wavelets. 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings. 2012. pp. 909-912 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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title = "Generalized total variation denoising via augmented Lagrangian cycle spinning with Haar wavelets",

abstract = "We consider the denoising of signals and images using regularized least-squares method. In particular, we propose a simple minimization algorithm for regularizers that are functions of the discrete gradient. By exploiting the connection of the discrete gradient with the Haar-wavelet transform, the n-dimensional vector minimization can be decoupled into n scalar minimizations. The proposed method can efficiently solve total-variation (TV) denoising by iteratively shrinking shifted Haar-wavelet transforms. Furthermore, the decoupling naturally lends itself to extensions beyond ℓ 1 regularizers.",

keywords = "cycle spinning, signal denoising, soft-thresholding, TV denoising",

author = "Ulugbek Kamilov and Emrah Bostan and Michael Unser",

year = "2012",

doi = "10.1109/ICASSP.2012.6288032",

language = "English",

isbn = "9781467300469",

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

pages = "909--912",

booktitle = "2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings",

note = "2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 ; Conference date: 25-03-2012 Through 30-03-2012",

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Kamilov, U, Bostan, E & Unser, M 2012, Generalized total variation denoising via augmented Lagrangian cycle spinning with Haar wavelets. in 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings., 6288032, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, pp. 909-912, 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012, Kyoto, Japan, 03/25/12. https://doi.org/10.1109/ICASSP.2012.6288032

Generalized total variation denoising via augmented Lagrangian cycle spinning with Haar wavelets. / Kamilov, Ulugbek; Bostan, Emrah; Unser, Michael.
2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings. 2012. p. 909-912 6288032 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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

TY - GEN

T1 - Generalized total variation denoising via augmented Lagrangian cycle spinning with Haar wavelets

AU - Kamilov, Ulugbek

AU - Bostan, Emrah

AU - Unser, Michael

PY - 2012

Y1 - 2012

N2 - We consider the denoising of signals and images using regularized least-squares method. In particular, we propose a simple minimization algorithm for regularizers that are functions of the discrete gradient. By exploiting the connection of the discrete gradient with the Haar-wavelet transform, the n-dimensional vector minimization can be decoupled into n scalar minimizations. The proposed method can efficiently solve total-variation (TV) denoising by iteratively shrinking shifted Haar-wavelet transforms. Furthermore, the decoupling naturally lends itself to extensions beyond ℓ 1 regularizers.

AB - We consider the denoising of signals and images using regularized least-squares method. In particular, we propose a simple minimization algorithm for regularizers that are functions of the discrete gradient. By exploiting the connection of the discrete gradient with the Haar-wavelet transform, the n-dimensional vector minimization can be decoupled into n scalar minimizations. The proposed method can efficiently solve total-variation (TV) denoising by iteratively shrinking shifted Haar-wavelet transforms. Furthermore, the decoupling naturally lends itself to extensions beyond ℓ 1 regularizers.

KW - cycle spinning

KW - signal denoising

KW - soft-thresholding

KW - TV denoising

UR - https://www.scopus.com/pages/publications/84867625323

U2 - 10.1109/ICASSP.2012.6288032

DO - 10.1109/ICASSP.2012.6288032

M3 - Conference contribution

AN - SCOPUS:84867625323

SN - 9781467300469

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

SP - 909

EP - 912

BT - 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings

T2 - 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012

Y2 - 25 March 2012 through 30 March 2012

ER -

Kamilov U, Bostan E, Unser M. Generalized total variation denoising via augmented Lagrangian cycle spinning with Haar wavelets. In 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings. 2012. p. 909-912. 6288032. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2012.6288032

Generalized total variation denoising via augmented Lagrangian cycle spinning with Haar wavelets

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