Novel uncertainty principles associated with 2D quaternion Fourier transforms

DOI10.1080/10652469.2015.1114482zbMath1333.62179OpenAlexW2311253441MaRDI QIDQ2790245

Kit Ian Kou, Yan Yang

Publication date: 3 March 2016

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2015.1114482

zbMATH Keywords

covariancequaternion Fourier transformHeisenberg's uncertainty principle

Mathematics Subject Classification ID

Image analysis in multivariate analysis (62H35) Functions of hypercomplex variables and generalized variables (30G35) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Analysis of variance and covariance (ANOVA) (62J10)

Related Items (13)

Tighter uncertainty principles based on quaternion Fourier transform ⋮ Novel uncertainty principles for two-sided quaternion linear canonical transform ⋮ The algebra of \(2D\) Gabor quaternionic offset linear canonical transform and uncertainty principles: the algebra of \(2D\) Gabor quaternionic offset LCT and uncertainty principles ⋮ Donoho-Stark's uncertainty principle for the quaternion Fourier transform ⋮ Quaternion hyperbolic Fourier transforms and uncertainty principles ⋮ Tighter Heisenberg-Weyl type uncertainty principle associated with quaternion wavelet transform ⋮ Quaternion Fourier and linear canonical inversion theorems ⋮ Plancherel theorem and quaternion Fourier transform for square integrable functions ⋮ Uncertainty principles for the quaternion linear canonical transform ⋮ Sharp inequalities for geometric Fourier transform and associated ambiguity function ⋮ Sharp Hausdorff-Young inequalities for the quaternion Fourier transforms ⋮ Quaternion windowed linear canonical transform of two-dimensional signals ⋮ Linear canonical wave packet transform

Cites Work

• On uncertainty principle for quaternionic linear canonical transform
• Extensions of the Heisenberg-Weyl inequality
• An uncertainty principle for quaternion Fourier transform
• Generalized Analytic Signals in Image Processing: Comparison, Theory and Applications
• Paley-Wiener theorems and uncertainty principles for the windowed linear canonical transform
• Information theoretic inequalities
• Uncertainty principles invariant under the fractional Fourier transform
• Quaternionic analysis
• Uncertainty Principle for Real Signals in the Linear Canonical Transform Domains
• A Tighter Uncertainty Principle for Linear Canonical Transform in Terms of Phase Derivative
• An uncertainty principle for real signals in the fractional Fourier transform domain
• Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT
• The Uncertainty Principle: Global, Local, or Both?
• Directional uncertainty principle for quaternion Fourier transform

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