Performance comparison of iterative reweighting methods for total variation regularization

Paul Rodríguez; Brendt Wohlberg

doi:10.1109/ICIP.2014.7025352

Performance comparison of iterative reweighting methods for total variation regularization

Paul Rodríguez, Brendt Wohlberg

Sección de Electricidad y Electrónica

Los Alamos National Laboratory Theoretical Division

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

6 Scopus citations

Abstract

Iteratively Reweighted Least Squares (IRLS) is a well-established method of optimizing ℓ^p norm problems such as Total Variation (TV) regularization. Within this general framework, there are several possible ways of constructing the weights and the form of the linear system that is iteratively solved as part of the algorithm. Many of these choices are equally reasonable from a theoretical perspective, and there has, thus far, been no systematic comparison between them. In this paper we provide such a comparison between the main choices in IRLS algorithms for ℓ¹- and ℓ²-TV denoising, finding that there is a significant variation in the computational cost and reconstruction quality of the different variants.

Original language	English
Title of host publication	2014 IEEE International Conference on Image Processing, ICIP 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1758-1762
Number of pages	5
ISBN (Electronic)	9781479957514
DOIs	https://doi.org/10.1109/ICIP.2014.7025352
State	Published - 28 Jan 2014

Publication series

Name	2014 IEEE International Conference on Image Processing, ICIP 2014

Keywords

Iteratively Reweighted Least Squares
Iteratively Reweighted Norm
Total Variation

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10.1109/ICIP.2014.7025352

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Rodríguez, P., & Wohlberg, B. (2014). Performance comparison of iterative reweighting methods for total variation regularization. In 2014 IEEE International Conference on Image Processing, ICIP 2014 (pp. 1758-1762). Article 7025352 (2014 IEEE International Conference on Image Processing, ICIP 2014). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICIP.2014.7025352

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abstract = "Iteratively Reweighted Least Squares (IRLS) is a well-established method of optimizing ℓp norm problems such as Total Variation (TV) regularization. Within this general framework, there are several possible ways of constructing the weights and the form of the linear system that is iteratively solved as part of the algorithm. Many of these choices are equally reasonable from a theoretical perspective, and there has, thus far, been no systematic comparison between them. In this paper we provide such a comparison between the main choices in IRLS algorithms for ℓ1- and ℓ2-TV denoising, finding that there is a significant variation in the computational cost and reconstruction quality of the different variants.",

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author = "Paul Rodr{\'i}guez and Brendt Wohlberg",

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doi = "10.1109/ICIP.2014.7025352",

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Rodríguez, P & Wohlberg, B 2014, Performance comparison of iterative reweighting methods for total variation regularization. in 2014 IEEE International Conference on Image Processing, ICIP 2014., 7025352, 2014 IEEE International Conference on Image Processing, ICIP 2014, Institute of Electrical and Electronics Engineers Inc., pp. 1758-1762. https://doi.org/10.1109/ICIP.2014.7025352

Performance comparison of iterative reweighting methods for total variation regularization. / Rodríguez, Paul; Wohlberg, Brendt.
2014 IEEE International Conference on Image Processing, ICIP 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 1758-1762 7025352 (2014 IEEE International Conference on Image Processing, ICIP 2014).

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

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N2 - Iteratively Reweighted Least Squares (IRLS) is a well-established method of optimizing ℓp norm problems such as Total Variation (TV) regularization. Within this general framework, there are several possible ways of constructing the weights and the form of the linear system that is iteratively solved as part of the algorithm. Many of these choices are equally reasonable from a theoretical perspective, and there has, thus far, been no systematic comparison between them. In this paper we provide such a comparison between the main choices in IRLS algorithms for ℓ1- and ℓ2-TV denoising, finding that there is a significant variation in the computational cost and reconstruction quality of the different variants.

AB - Iteratively Reweighted Least Squares (IRLS) is a well-established method of optimizing ℓp norm problems such as Total Variation (TV) regularization. Within this general framework, there are several possible ways of constructing the weights and the form of the linear system that is iteratively solved as part of the algorithm. Many of these choices are equally reasonable from a theoretical perspective, and there has, thus far, been no systematic comparison between them. In this paper we provide such a comparison between the main choices in IRLS algorithms for ℓ1- and ℓ2-TV denoising, finding that there is a significant variation in the computational cost and reconstruction quality of the different variants.

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Rodríguez P, Wohlberg B. Performance comparison of iterative reweighting methods for total variation regularization. In 2014 IEEE International Conference on Image Processing, ICIP 2014. Institute of Electrical and Electronics Engineers Inc. 2014. p. 1758-1762. 7025352. (2014 IEEE International Conference on Image Processing, ICIP 2014). doi: 10.1109/ICIP.2014.7025352

Performance comparison of iterative reweighting methods for total variation regularization

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