Eigenvalues of Quaternion Tensors with Applications to Color Video Processing

He, Zhuo-Heng; Wang, Xiangxiang; Zhao, Yun-Fan

doi:10.1007/s10915-022-02058-5

Cited by 17 publications

(1 citation statement)

References 38 publications

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“…Additionally, quaternions are used to represent color video signals so as to retain correlation between the three channels of red, green, blue. Therefore, they have been widely employed in color imaging and color videos in the literature (Sangwine, 1996;He et al, 2023). They are also suitable for describing translations, rotations of a rigid body (Arena et al, 1998;Caccavale et al, 1999).…”

Section: Introductionmentioning

confidence: 99%

A Block Conjugate Gradient Method for Quaternion Linear

ŞİMŞEK¹,

KÖRÜKÇÜ²

2023

Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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This study aims at the simultaneous solution of several quaternion linear systems with the same Hermitian and positive definite coefficient matrix by employing the conjugate gradient method. We consider the setting when the quaternion Hermitian positive definite coefficient matrix at hand is very large so that direct methods are not applicable. In the study, we first transform linear quaternion systems into real linear systems. Then a block conjugate gradient method is applied to the real linear systems. The solution obtained after applying the conjugate gradient method is the real representation of the solution of the original quaternion problem. Thus, a conversion of this real solution to the quaternion setting is performed in the end.

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