Quaternion and Clifford Fourier Transforms and Wavelets

Editors:

ISBN: 978-3-0348-0602-2 (Print) 978-3-0348-0603-9 (Online)

Table of contents (16 chapters)

  1. Front Matter

    Pages i-xxvii

  2. Quaternions

    1. Front Matter

      Pages 1-1

    2. No Access

      Chapter

      Pages 3-14

      Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis

    3. No Access

      Chapter

      Pages 15-39

      The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations

    4. No Access

      Chapter

      Pages 41-56

      Quaternionic Spectral Analysis of Non-Stationary Improper Complex Signals

    5. No Access

      Chapter

      Pages 57-83

      Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions

    6. No Access

      Chapter

      Pages 85-104

      Bochner’s Theorems in the Framework of Quaternion Analysis

    7. No Access

      Chapter

      Pages 105-120

      Bochner–Minlos Theorem and Quaternion Fourier Transform

  3. Clifford Algebra

    1. Front Matter

      Pages 121-121

    2. No Access

      Chapter

      Pages 123-153

      Square Roots of –1 in Real Clifford Algebras

    3. No Access

      Chapter

      Pages 155-176

      A General Geometric Fourier Transform

    4. No Access

      Chapter

      Pages 177-195

      Clifford–Fourier Transform and Spinor Representation of Images

    5. No Access

      Chapter

      Pages 197-219

      Analytic Video (2D + t) Signals Using Clifford–Fourier Transforms in Multiquaternion Grassmann–Hamilton–Clifford Algebras

    6. No Access

      Chapter

      Pages 221-246

      Generalized Analytic Signals in Image Processing: Comparison, Theory and Applications

    7. No Access

      Chapter

      Pages 247-268

      Colour Extension of Monogenic Wavelets with Geometric Algebra: Application to Color Image Denoising

    8. No Access

      Chapter

      Pages 269-284

      Seeing the Invisible and Maxwell’s Equations

    9. No Access

      Chapter

      Pages 285-298

      A Generalized Windowed Fourier Transform in Real Clifford Algebra Cl 0,n

    10. No Access

      Chapter

      Pages 299-319

      The Balian–Low Theorem for the Windowed Clifford–Fourier Transform

    11. No Access

      Chapter

      Pages 321-332

      Sparse Representation of Signals in Hardy Space

  4. Back Matter

    Pages 333-338