Quaternion fourier transforms for signal and image processing / Todd A. Ell, Nicolas Le Bihan, Stephen J. Sangwine.

Format:

Book

Author/Creator:

Ell, Todd A., author.

Le Bihan, Nicolas, author.

Sangwine, Stephen J., author.

Series:

Focus series in digital signal and image processing.

Focus Digital Signal and Image Processing Series, 2051-249X

Language:

English

Subjects (All):

Signal processing.

Image processing.

Quaternions.

Physical Description:

1 online resource (160 p.)

Edition:

1st ed.

Place of Publication:

London ; Hoboken, New Jersey : ISTE : Wiley, 2014.

Language Note:

English

Summary:

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.

Contents:

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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781118930908

1118930908

9781118930922

1118930924

9781118930915

1118930916

OCLC:

881416956