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Quaternion Fourier and linear canonical inversion theorems
Hu, Xiao-Xiao; Kou, Kit Ian
2017-05
Source PublicationMATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN0170-4214
Volume40Issue:7Pages:2421-2440
Abstract

The quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In addition, understanding the QFT paves the way for understanding other integral transform, such as the quaternion fractional Fourier transform, quaternion linear canonical transform, and quaternion Wigner-Ville distribution. The aim of this paper is twofold: first to provide some of the theoretical background regarding the quaternion bound variation function. We then apply it to derive the quaternion Fourier and linear canonical inversion formulas. Secondly, to provide some in tuition for how the quaternion Fourier and linear canonical inversion theorems work on the absolutely integrable function space. Copyright (c) 2016 John Wiley & Sons, Ltd.

KeywordInversion Theorem Functions Of Bound Variation Quaternion Fourier Transform
DOIhttps://doi.org/10.1002/mma.4148
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000399668000009
PublisherWILEY
The Source to ArticleWOS
Fulltext Access
Citation statistics
Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorKou, Kit Ian
AffiliationDepartment of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macau, China
First Author AffilicationFaculty of Science and Technology
Corresponding Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Hu, Xiao-Xiao,Kou, Kit Ian. Quaternion Fourier and linear canonical inversion theorems[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2017,40(7):2421-2440.
APA Hu, Xiao-Xiao,&Kou, Kit Ian.(2017).Quaternion Fourier and linear canonical inversion theorems.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,40(7),2421-2440.
MLA Hu, Xiao-Xiao,et al."Quaternion Fourier and linear canonical inversion theorems".MATHEMATICAL METHODS IN THE APPLIED SCIENCES 40.7(2017):2421-2440.
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