Residential College | false |
Status | 已發表Published |
Quaternion Fourier and linear canonical inversion theorems | |
Hu, Xiao-Xiao; Kou, Kit Ian | |
2017-05 | |
Source Publication | MATHEMATICAL METHODS IN THE APPLIED SCIENCES |
ISSN | 0170-4214 |
Volume | 40Issue: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. |
Keyword | Inversion Theorem Functions Of Bound Variation Quaternion Fourier Transform |
DOI | 10.1002/mma.4148 |
URL | View the original |
Indexed By | SCIE |
Language | 英語English |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000399668000009 |
Publisher | WILEY |
The Source to Article | WOS |
Scopus ID | 2-s2.0-84992497470 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Corresponding Author | Kou, Kit Ian |
Affiliation | Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macau, China |
First Author Affilication | Faculty of Science and Technology |
Corresponding Author Affilication | Faculty 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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