On extending the ADMM algorithm to the quaternion algebra setting
- Author
- Srdan Lazendic (UGent) , Hendrik De Bie (UGent) and Aleksandra Pizurica (UGent)
- Organization
- Abstract
- Many image and signal processing problems benefit from quaternion based models, due to their property of processing different features simultaneously. Recently the quaternion algebra model has been combined with the dictionary learning and sparse representation models. This led to solving versatile optimization problems over the quaternion algebra. Since the quaternions form a noncommutative algebra, calculation of the gradient of the quaternion objective function is usually fairly complex. This paper aims to present a generalization of the augmented directional method of multipliers over the quaternion algebra, while employing the results from the recently introduced generalized HR (GHR) calculus. Furthermore, we consider the convex optimization problems of real functions of quaternion variable.
- Keywords
- Numerical optimization, ADMM, Quaternions
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8704377
- MLA
- Lazendic, Srdan, et al. “On Extending the ADMM Algorithm to the Quaternion Algebra Setting.” IEICE PROCEEDING SERIES, edited by Dragana Krstic and Maciej Piechowiak, vol. 64, IEICE Europe Section, 2021, doi:10.34385/proc.64.ICTF2020_paper_26.
- APA
- Lazendic, S., De Bie, H., & Pizurica, A. (2021). On extending the ADMM algorithm to the quaternion algebra setting. In D. Krstic & M. Piechowiak (Eds.), IEICE PROCEEDING SERIES (Vol. 64). https://doi.org/10.34385/proc.64.ICTF2020_paper_26
- Chicago author-date
- Lazendic, Srdan, Hendrik De Bie, and Aleksandra Pizurica. 2021. “On Extending the ADMM Algorithm to the Quaternion Algebra Setting.” In IEICE PROCEEDING SERIES, edited by Dragana Krstic and Maciej Piechowiak. Vol. 64. IEICE Europe Section. https://doi.org/10.34385/proc.64.ICTF2020_paper_26.
- Chicago author-date (all authors)
- Lazendic, Srdan, Hendrik De Bie, and Aleksandra Pizurica. 2021. “On Extending the ADMM Algorithm to the Quaternion Algebra Setting.” In IEICE PROCEEDING SERIES, ed by. Dragana Krstic and Maciej Piechowiak. Vol. 64. IEICE Europe Section. doi:10.34385/proc.64.ICTF2020_paper_26.
- Vancouver
- 1.Lazendic S, De Bie H, Pizurica A. On extending the ADMM algorithm to the quaternion algebra setting. In: Krstic D, Piechowiak M, editors. IEICE PROCEEDING SERIES. IEICE Europe Section; 2021.
- IEEE
- [1]S. Lazendic, H. De Bie, and A. Pizurica, “On extending the ADMM algorithm to the quaternion algebra setting,” in IEICE PROCEEDING SERIES, Nis, Serbia, Virtual, 2021, vol. 64.
@inproceedings{8704377,
abstract = {{Many image and signal processing problems benefit from quaternion based models, due to their property of processing different features simultaneously. Recently the quaternion algebra model has been combined with the dictionary learning and sparse representation models. This led to solving versatile optimization problems over the quaternion algebra. Since the quaternions form a noncommutative algebra, calculation of the gradient of the quaternion objective function is usually fairly complex. This paper aims to present a generalization of the augmented directional method of multipliers over the quaternion algebra, while employing the results from the recently introduced generalized HR (GHR) calculus. Furthermore, we consider the convex optimization problems of real functions of quaternion variable.}},
articleno = {{26}},
author = {{Lazendic, Srdan and De Bie, Hendrik and Pizurica, Aleksandra}},
booktitle = {{IEICE PROCEEDING SERIES}},
editor = {{Krstic, Dragana and Piechowiak, Maciej}},
isbn = {{9788393260287}},
issn = {{2188-5079}},
keywords = {{Numerical optimization,ADMM,Quaternions}},
language = {{eng}},
location = {{Nis, Serbia, Virtual}},
pages = {{4}},
publisher = {{IEICE Europe Section}},
title = {{On extending the ADMM algorithm to the quaternion algebra setting}},
url = {{http://doi.org/10.34385/proc.64.ICTF2020_paper_26}},
volume = {{64}},
year = {{2021}},
}
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