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Quaternion Fourier Transforms for Signal and Image Processing.
Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book's attention to mat...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
Wiley,
2014.
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| Colección: | FOCUS Series.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title Page; Copyright; Contents; Nomenclature; Preface; Introduction; Chapter 1. Quaternion Algebra; 1.1. Definitions; 1.2. Properties; 1.3. Exponential and logarithm of a quaternion; 1.3.1. Exponential of a pure quaternion; 1.3.2. Exponential of a full quaternion; 1.3.3. Logarithm of a quaternion; 1.4. Representations; 1.4.1. Polar forms; 1.4.2. The Cj-pair notation; 1.4.3. R and C matrix representations; 1.5. Powers of a quaternion; 1.6. Subfields; Chapter 2. Geometric Applications; 2.1. Euclidean geometry (3D and 4D); 2.1.1. 3D reflections; 2.1.2. 3D rotations; 2.1.3. 3D shears.
- 2.1.4. 3D dilations2.1.5. 4D reflections; 2.1.6. 4D rotations; 2.2. Spherical geometry; 2.3. Projective space (3D); 2.3.1. Systems of linear quaternion functions; 2.3.2. Projective transformations; Chapter 3. Quaternion Fourier Transforms; 3.1. 1D quaternion Fourier transforms; 3.1.1. Definitions; 3.1.2. Basic transform pairs; 3.1.3. Decompositions; 3.1.4. Inter-relationships between definitions; 3.1.5. Convolution and correlation theorems; 3.2. 2D quaternion Fourier transforms; 3.2.1. Definitions; 3.2.2. Basic transform pairs; 3.2.3. Decompositions.
- 3.2.4. Inter-relationships between definitions3.3. Computational aspects; 3.3.1. Coding; 3.3.2. Verification; 3.3.3. Verification of transforms; Chapter 4. Signal And Image Processing; 4.1. Generalized convolution; 4.1.1. Classical grayscale image convolution filters; 4.1.2. Color images as quaternion arrays; 4.1.3. Quaternion convolution; 4.1.4. Quaternion image spectrum; 4.2. Generalized correlation; 4.2.1. Classical correlation and phase correlation; 4.2.2. Quaternion correlation; 4.2.3. Quaternion phase correlation; 4.3. Instantaneous phase and amplitude of complex signals.
- 4.3.1. Important properties of 1D QFT of a complex signal z(t)4.3.2. Hilbert transform and right-sided quaternion spectrum; 4.3.3. The quaternion signal associated with a complex signal; 4.3.4. Instantaneous amplitude and phase; 4.3.5. The instantaneous frequency of a complex signal; 4.3.6. Examples; 4.3.7. The quaternion Wigner-Ville distribution of a complex signal; 4.3.8. Time marginal; 4.3.9. The mean frequency formula; Bibliography; Index; Supplemental Images.