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Novel uncertainty principles associated with 2D quaternion Fourier transforms
Yang Y.2; Ian Kou K.1
2016-03-03
Source PublicationIntegral Transforms and Special Functions
ISSN14768291 10652469
Volume27Issue:3Pages:213-226
Abstract

The quaternion Fourier transform has been widely employed in the colour image processing. The use of quaternions allow the analysis of colour images as vector fields. In this paper, the right-sided quaternion Fourier transform and its properties are reviewed. Using the polar form of quaternions, two novel uncertainty principles associated with covariance are established. They prescribe the lower bounds with covariances on the products of the effective widths of quaternionic signals in the space and frequency domains. The results generalize the Heisenberg's uncertainty principle to the 2D quaternionic space.

KeywordCovariance Heisenberg's Uncertainty Principle Quaternion Fourier Transform
DOI10.1080/10652469.2015.1114482
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000376168900004
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Citation statistics
Cited Times [WOS]:12   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Universidade de Macau
2.Sun Yat-Sen University
Recommended Citation
GB/T 7714
Yang Y.,Ian Kou K.. Novel uncertainty principles associated with 2D quaternion Fourier transforms[J]. Integral Transforms and Special Functions,2016,27(3):213-226.
APA Yang Y.,&Ian Kou K..(2016).Novel uncertainty principles associated with 2D quaternion Fourier transforms.Integral Transforms and Special Functions,27(3),213-226.
MLA Yang Y.,et al."Novel uncertainty principles associated with 2D quaternion Fourier transforms".Integral Transforms and Special Functions 27.3(2016):213-226.
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