Quaternion and Clifford Fourier Transforms and Wavelets

Part I. Quaternions

1. Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis
Todd Anthony Ell

2. The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations
Eckhard Hitzer, Stephen J. Sangwine

3. Quaternionic Spectral Analysis of Non-Stationary Improper Complex Signals
Nicolas Le Bihan, Stephen J. Sangwine

4. Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions
E. Ulises Moya-Sánchez, E. Bayro-Corrochano

5. Bochner’s Theorems in the Framework of Quaternion Analysis
S. Georgiev, J. Morais

6. Bochner–Minlos Theorem and Quaternion Fourier Transform
S. Georgiev, J. Morais, K. I. Kou, W. Sprößig

Part II. Clifford Algebra

7. Square Roots of –1 in Real Clifford Algebras
Eckhard Hitzer, Jacques Helmstetter, Rafał Abłamowicz

8. A General Geometric Fourier Transform
Roxana Bujack, Gerik Scheuermann, Eckhard Hitzer

9. Clifford–Fourier Transform and Spinor Representation of Images
Thomas Batard, Michel Berthier

10. Analytic Video (2D + t) Signals Using Clifford–Fourier Transforms in Multiquaternion Grassmann–Hamilton–Clifford Algebras
P. R. Girard, R. Pujol, P. Clarysse, A. Marion, R. Goutte, P. Delachartre

11. Generalized Analytic Signals in Image Processing: Comparison, Theory and Applications
Swanhild Bernstein, Jean-Luc Bouchot, Martin Reinhardt, Bettina Heise

12. Colour Extension of Monogenic Wavelets with Geometric Algebra: Application to Color Image Denoising
Raphaël Soulard, Philippe Carré

13. Seeing the Invisible and Maxwell’s Equations
Swanhild Bernstein

14. A Generalized Windowed Fourier Transform in Real Clifford Algebra Cl

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Mawardi Bahri

15. The Balian–Low Theorem for the Windowed Clifford–Fourier Transform
Yingxiong Fu, Uwe Kähler, Paula Cerejeiras

16. Sparse Representation of Signals in Hardy Space
Shuang Li, Tao Qian

Avainsanat: Mathematics, Number Theory, Linear and Multilinear Algebras, Matrix Theory, Numerical Analysis, Fourier Analysis, Image Processing and Computer Vision