A comparison of the computational performance of Iteratively Reweighted Least Squares and alternating minimization algorithms for ℓ1 inverse problems

Paul Rodríguez; Brendt Wohlberg

doi:10.1109/ICIP.2012.6467548

A comparison of the computational performance of Iteratively Reweighted Least Squares and alternating minimization algorithms for ℓ₁ inverse problems

Paul Rodríguez, Brendt Wohlberg

Los Alamos National Laboratory Theoretical Division

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

5 Scopus citations

Abstract

Alternating minimization algorithms with a shrinkage step, derived within the Split Bregman (SB) or Alternating Direction Method of Multipliers (ADMM) frameworks, have become very popular for ℓ¹-regularized problems, including Total Variation and Basis Pursuit Denoising. It appears to be generally assumed that they deliver much better computational performance than older methods such as Iteratively Reweighted Least Squares (IRLS). We show, however, that IRLS type methods are computationally competitive with SB/ADMM methods for a variety of problems, and in some cases outperform them.

Original language	English
Title of host publication	2012 IEEE International Conference on Image Processing, ICIP 2012 - Proceedings
Pages	3069-3072
Number of pages	4
DOIs	https://doi.org/10.1109/ICIP.2012.6467548
State	Published - 2012
Event	2012 19th IEEE International Conference on Image Processing, ICIP 2012 - Lake Buena Vista, FL, United States Duration: 30 Sep 2012 → 3 Oct 2012

Publication series

Name	Proceedings - International Conference on Image Processing, ICIP
ISSN (Print)	1522-4880

Conference

Conference	2012 19th IEEE International Conference on Image Processing, ICIP 2012
Country/Territory	United States
City	Lake Buena Vista, FL
Period	30/09/12 → 3/10/12

Keywords

Inverse Problems
Iteratively Reweighted Least Squares
Split-Bregman
Total Variation

Access to Document

10.1109/ICIP.2012.6467548

Cite this

Rodríguez, P., & Wohlberg, B. (2012). A comparison of the computational performance of Iteratively Reweighted Least Squares and alternating minimization algorithms for ℓ₁ inverse problems. In 2012 IEEE International Conference on Image Processing, ICIP 2012 - Proceedings (pp. 3069-3072). Article 6467548 (Proceedings - International Conference on Image Processing, ICIP). https://doi.org/10.1109/ICIP.2012.6467548

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abstract = "Alternating minimization algorithms with a shrinkage step, derived within the Split Bregman (SB) or Alternating Direction Method of Multipliers (ADMM) frameworks, have become very popular for ℓ1-regularized problems, including Total Variation and Basis Pursuit Denoising. It appears to be generally assumed that they deliver much better computational performance than older methods such as Iteratively Reweighted Least Squares (IRLS). We show, however, that IRLS type methods are computationally competitive with SB/ADMM methods for a variety of problems, and in some cases outperform them.",

keywords = "Inverse Problems, Iteratively Reweighted Least Squares, Split-Bregman, Total Variation",

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series = "Proceedings - International Conference on Image Processing, ICIP",

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Rodríguez, P & Wohlberg, B 2012, A comparison of the computational performance of Iteratively Reweighted Least Squares and alternating minimization algorithms for ℓ₁ inverse problems. in 2012 IEEE International Conference on Image Processing, ICIP 2012 - Proceedings., 6467548, Proceedings - International Conference on Image Processing, ICIP, pp. 3069-3072, 2012 19th IEEE International Conference on Image Processing, ICIP 2012, Lake Buena Vista, FL, United States, 30/09/12. https://doi.org/10.1109/ICIP.2012.6467548

A comparison of the computational performance of Iteratively Reweighted Least Squares and alternating minimization algorithms for ℓ₁ inverse problems. / Rodríguez, Paul; Wohlberg, Brendt.
2012 IEEE International Conference on Image Processing, ICIP 2012 - Proceedings. 2012. p. 3069-3072 6467548 (Proceedings - International Conference on Image Processing, ICIP).

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

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Rodríguez P, Wohlberg B. A comparison of the computational performance of Iteratively Reweighted Least Squares and alternating minimization algorithms for ℓ₁ inverse problems. In 2012 IEEE International Conference on Image Processing, ICIP 2012 - Proceedings. 2012. p. 3069-3072. 6467548. (Proceedings - International Conference on Image Processing, ICIP). doi: 10.1109/ICIP.2012.6467548