Summary
IEICE Information and Communication Technology Forum
2020
Session Number:ICTF_4
Session:
Number:ICTF2020_paper_26
On Extending the ADMM Algorithm to the Quaternion Algebra Setting
Srdan Lazendic, Hendrik De Bie, Aleksandra Pizurica,
pp.-
Publication Date:2021/03/24
Online ISSN:2188-5079
DOI:10.34385/proc.64.ICTF2020_paper_26
Summary:
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 eneralization 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.