Quaternion and Clifford Fourier Transforms and Wavelets
Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex...
| Other Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser
2013, 2013
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| Edition: | 1st ed. 2013 |
| Series: | Trends in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Preface.- History of Quaternion and Clifford-Fourier Transforms and Wavelets
- Part I: Quaternions.- 1 Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis.- 2 The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations.- 3 Quaternionic Spectral Analysis of Non-Stationary Improper Complex Signals.- 4 Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions.- 5 Bochner’s Theorems in the Framework of Quaternion Analysis.- 6 Bochner-Minlos Theorem and Quaternion Fourier Transform
- Part II: Clifford Algebra.- 7 Square Roots of -1 in Real Clifford Algebras.- 8 A General Geometric Fourier Transform.- 9 Clifford-Fourier Transform and Spinor Representation of Images
- 10 Analytic Video (2D+t) Signals Using Clifford-Fourier Transforms in Multiquaternion Grassmann-Hamilton-Clifford Algebras
- 11 Generalized Analytic Signals in Image Processing: Comparison, Theory and Applications
- 12 Color Extension of Monogenic Wavelets with Geometric Algebra: Application to Color Image Denoising
- 13 Seeing the Invisible and Maxwell’s Equations
- 14 A Generalized Windowed Fourier Transform in Real Clifford Algebra Cl_{0,n}
- 15 The Balian-Low theorem for the Windowed Clifford-Fourier Transform
- 16 Sparse Representation of Signals in Hardy Space. - Index