Quaternion tensor singular value decomposition using a flexible transform-based approach

doi:10.1016/j.sigpro.2022.108910

Residential College	false
Status	已發表Published
	Quaternion tensor singular value decomposition using a flexible transform-based approach
	Miao, Jifei 1; Kou, Kit Ian 2
	2023-05-01
Source Publication	Signal Processing
ISSN	0165-1684
Volume	206
Abstract	A flexible transform-based tensor product named ★-product for Lth-order (L≥3) quaternion tensors is proposed. Based on the ★-product, we define the corresponding singular value decomposition named TQt-SVD and the rank named TQt-rank of the Lth-order (L≥3) quaternion tensor. Furthermore, with orthogonal quaternion transformations, the TQt-SVD can provide the best TQt-rank-s approximation of any Lth-order (L≥3) quaternion tensor. On the other side, since a color pixel with RGB channels can be well encoded as a pure quaternion, the proposed TQt-SVD, therefore, becomes a new mathematical tool for many color image processing tasks. In the experiments, we have verified the effectiveness of the proposed TQt-SVD in the application of the best TQt-rank-s approximation for color videos represented by third-order quaternion tensors.
Keyword	Color image Color video Low-rank approximation Quaternion tensor singular value decomposition
DOI	10.1016/j.sigpro.2022.108910
URL	View the original
Language	英語English
Scopus ID	2-s2.0-85145202690
Fulltext Access	View Full-Text via DOI View Full-Text via Web of Science View Full-Text via Scopus
Citation statistics	Cited Times [WOS]:7 [WOS Record] [Related Records in WOS]
Document Type	Journal article
Collection	University of Macau
Affiliation	1.School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan, 650091, China 2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau 999078, China
Recommended Citation GB/T 7714	Miao, Jifei,Kou, Kit Ian. Quaternion tensor singular value decomposition using a flexible transform-based approach[J]. Signal Processing, 2023, 206.
APA	Miao, Jifei., & Kou, Kit Ian (2023). Quaternion tensor singular value decomposition using a flexible transform-based approach. Signal Processing, 206.
MLA	Miao, Jifei,et al."Quaternion tensor singular value decomposition using a flexible transform-based approach".Signal Processing 206(2023).

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