Quaternion Fourier Transforms for Signal and Image Processing 1st Edition by Todd Ell, Nicolas Le Bihan, Stephen Sangwine ISBN 1848214782 978-1848214781

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ISBN 10: 1848214782
ISBN 13: 978-1848214781
Author:  Todd Ell, Nicolas Le Bihan, Stephen Sangwine 

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 mathematical concepts, imaging applications, and Matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers.

Quaternion Fourier Transforms for Signal and Image Processing 1st Table of contents:

I.1. Fourier analysis

I.2. Quaternions

I.3. Quaternion Fourier transforms

I.4. Signal and image processing

I.5. Other hypercomplex algebras

I.6. Practical application

I.7. Overview of the remaining chapters

1 Quaternion Algebra

1.1. Definitions

1.2. Properties

1.3. Exponential and logarithm of a quaternion

1.4. Representations

1.5. Powers of a quaternion

1.6. Subfields

2 Geometric Applications

2.1. Euclidean geometry (3D and 4D)

2.2. Spherical geometry

2.3. Projective space (3D)

3 Quaternion Fourier Transforms

3.1. 1D quaternion Fourier transforms

3.2. 2D quaternion Fourier transforms

3.3. Computational aspects

4 Signal And Image Processing

4.1. Generalized convolution

4.2. Generalized correlation

4.3. Instantaneous phase and amplitude of complex signals

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Tags: Todd Ell, Nicolas Le Bihan, Stephen Sangwine, Quaternion Fourier, Image Processing