Quaternionic Integral Transforms

Name: Quaternionic Integral Transforms | A Machine-Generated Literature Overview
Brand: Birkhäuser
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A Machine-Generated Literature Overview

Eckhard Hitzer(Herausgeber*in)

Birkhäuser (Verlag)

Erschienen am 8. August 2023

XI, 177 Seiten

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Inhalt

Intro
Foreword
Introduction
Contents
Quaternion Fourier Transform
1 Theory
1.1 General Theory
1.1.1 Quaternion Fourier Transform on Quaternion Fields and Generalizations
1.1.2 General Two-Sided Quaternion Fourier Transform, Convolution and Mustard Convolution
1.1.3 Quaternionic Wiener-Khinchine Theorems and Spectral Representation of Convolution with Steerable Two-Sided Quaternion Fourier Transform
1.1.4 The Quaternion Domain Fourier Transform and Its Properties
1.1.5 Multilinear Localization Operators Associated to Quaternion Fourier Transforms
1.1.6 Quaternion Fourier Transform and Generalized Lipschitz Classes
1.1.7 The Quaternion Fourier and Wavelet Transforms on Spaces of Functions and Distributions
1.2 Special Theorems
1.2.1 Titchmarsh's Theorem and Some Remarks Concerning the Right-Sided Quaternion Fourier Transform
1.2.2 Paley-Wiener and Boas Theorems for the Quaternion Fourier Transform
1.2.3 Paley-Wiener Theorems for the Two-Sided Quaternion Fourier Transform
1.2.4 Bochner's Theorems in the Framework of Quaternion Analysis
1.2.5 Bochner-Minlos Theorem and Quaternion Fourier Transform
1.2.6 Hyers-Ulam Stability of Linear Quaternion-Valued Differential Equations with Constant Coefficients via Fourier Transform
1.2.7 Complex Interpolation of Lp(C, H) Spaces with Respect to Cullen-Regular
2 Uncertainty
2.1 Directional Uncertainty Principle for Quaternion Fourier Transform
2.2 The Uncertainty Principle for the Two-Sided Quaternion Fourier Transform
2.3 A New Uncertainty Principle Related to the Generalized Quaternion Fourier Transform
2.4 Miyachi's Theorem for the Quaternion Fourier Transform
2.5 Tighter Uncertainty Principles Based on Quaternion Fourier Transform
2.6 A Modified Uncertainty Principle for Two-Sided Quaternion Fourier Transform
2.7 Donoho-Stark's Uncertainty Principle for the Quaternion Fourier Transform
2.8 Beurling's Theorem for the Quaternion Fourier Transform
2.9 Uncertainty Principle for the Two Sided Quaternion Windowed Fourier Transform
3 Signal Processing
3.1 Sampling Formulas for Non-bandlimited Quaternionic Signals
3.2 Sampling Formulas for 2D Quaternionic Signals Associated with Various Quaternion Fourier and Linear Canonical Transforms
3.3 Quaternionic Spectral Analysis of Non-stationary Improper Complex Signals
3.4 Many-Parameter Quaternion Fourier Transforms for Intelligent OFDM Telecommunication System
3.5 Intelligent OFDM Telecommunication Systems Based on Many-Parameter Complex or Quaternion Fourier Transforms
3.6 Quaternion Fourier Descriptors for the Preprocessing and Recognition of Spoken Words Using Images of Spatiotemporal Representations
4 Image Processing
4.1 The Quaternion-Fourier Transform and Applications
4.2 Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis
4.3 A Robust Color Edge Detection Algorithm Based on the Quaternion Hardy Filter
4.4 Denoising Color Images Based on Local Orientation Estimation and CNN Classifier
4.5 Rotation Invariant Features for Color Texture Classification and Retrieval Under Varying Illumination
4.6 Quaternion-Based Texture Analysis of Multiband Satellite Images: Application to the Estimation of Aboveground Biomass in the East Region of Cameroon
5 Watermarking
5.1 DWT-DQFT-Based Color Image Blind Watermark with QR Decomposition
5.2 A Robust Blind Watermarking Scheme for Color Images Using Quaternion Fourier Transform
5.3 New Watermarking Algorithm Utilizing Quaternion Fourier Transform with Advanced Scrambling and Secure Encryption
5.4 Quaternion Discrete Fractional Random Transform for Color Image Adaptive Watermarking
6 Saliency
6.1 Bottom-Up Saliency Detection Model Based on Amplitude Spectrum
6.2 Saliency Detection for Stereoscopic 3D Images in the Quaternion Frequency Domain
6.3 Quaternion-Based Spectral Saliency Detection for Eye Fixation Prediction
6.4 Biological Plausibility of Spectral Domain Approach for Spatiotemporal Visual Saliency
7 Motion and Video
7.1 Moving Target Tracking Based on Pulse Coupled Neural Network and Optical Flow
7.2 Fast Correction Visual Tracking via Feedback Mechanism
7.3 Desert Vehicle Detection Based on Adaptive Visual Attention and Neural Network
7.4 Analytic Video (2D + T) Signals Using Clifford-Fourier Transforms in Multiquaternion Grassmann-Hamilton-Clifford Algebras
References
Quaternion Wavelet Transform (QWT)
1 Background and Theory
1.1 Background for QWT
1.1.1 QWT: Retrospective and New Applications
1.1.2 The Theory and Use of the Quaternion Wavelet Transform
1.1.3 Discrete Wavelets with Quaternion and Clifford Coefficients
1.1.4 Quaternion-Valued Smooth Compactly Supported Orthogonal Wavelets with Symmetry
1.1.5 The Continuous Quaternion Algebra-Valued Wavelet Transform and the Associated Uncertainty Principle
1.2 Theoretical Developments for the QWT
1.2.1 Linear Canonical Wavelet Transform in Quaternion Domains
1.2.2 The Quaternion Fourier and Wavelet Transforms on Spaces of Functions and Distributions
1.2.3 Wavelet Transform of Dini Lipschitz Functions on the Quaternion Algebra
1.2.4 Equivalence Between K-Functionals and Modulus of Smoothness on the Quaternion Algebra
2 Image Processing
2.1 Image Processing, Colorization and Sharpness
2.1.1 Multi-Resolution Image Analysis Using the Quaternion Wavelet Transform
2.1.2 Quaternion Atomic Function for Image Processing
2.1.3 Colorization Using Quaternion Algebra with Automatic Scribble Generation
2.1.4 The Image Sharpness Metric via Gaussian Mixture Modeling of the Quaternion Wavelet Transform Phase Coefficients with Applications
2.2 Image Denoising and Saliency
2.2.1 Image Denoising via Modified Multiple-Step Local Wiener Filter and Quaternion Wavelet Transform
2.2.2 Image Denoising Using Normal Inverse Gaussian Model in Quaternion Wavelet Domain
2.2.3 Image Denoising Using Fractional Quaternion Wavelet Transform
2.2.4 Information-Based Scale Saliency Methods with Wavelet Sub-band Energy Density Descriptors
3 Watermarking and Forensic Features
3.1 A Novel Color Image Watermarking Algorithm Based on QWT and DCT
3.1.1 A Novel Robust Image Watermarking in Quaternion Wavelet Domain Based on Superpixel Segmentation
3.1.2 Optimal Image Watermarking Scheme Based on Chaotic Map and Quaternion Wavelet Transform
3.1.3 A Robust Color Image Watermarking Algorithm Against Rotation Attacks
3.1.4 Forensics Feature Analysis in Quaternion Wavelet Domain for Distinguishing Photographic Images and Computer Graphics
4 Medical Images and Tracking
4.1 Adopting Quaternion Wavelet Transform to Fuse Multi-Modal Medical Images
4.1.1 Correlative Feature Selection for Multimodal Medical Image Fusion Through QWT
4.1.2 Skin Lesion Image Classification Using Sparse Representation in Quaternion Wavelet Domain
4.1.3 A Fast Quaternion Wavelet-Based Motion Compensated Frame Rate Up-Conversion with Fuzzy Smoothing: Application to Echocardiography Temporal Enhancement
4.1.4 Visual Objects Tracking and Identification Based on Reduced Quaternion Wavelet Transform
References
Further Quaternion Integral Transforms
1 Quaternionic Curvelets, Ridgelets and Shearlets
1.1 Uncertainty Principles for the Continuous Quaternion Shearlet Transform
1.2 Quaternion Ridgelet Transform and Curvelet Transform
1.3 Infrared Small Target Detection Based on Non-subsampled Shearlet Transform and Phase Spectrum of Quaternion Fourier Transform
2 Quaternionic Linear Canonical Transforms (QLCT)
2.1 QLCT Theorems
2.1.1 Plancherel Theorems of Quaternion Hilbert Transforms Associated with Linear Canonical Transforms
2.1.2 Jackson Theorems for the Quaternion Linear Canonical Transform
2.2 QLCT and Uncertainty
2.2.1 Novel Uncertainty Principles for Two-Sided Quaternion Linear Canonical Transform
2.2.2 On Uncertainty Principle for the Two-Sided Quaternion Linear Canonical Transform
2.2.3 Uncertainty Principles for the Two-Sided Quaternion Linear Canonical Transform
2.2.4 Uncertainty Principle for the Two-Sided Quaternion Windowed Linear Canonical Transform
2.3 QLCT Applications
2.3.1 Sampling Formulas for Non-bandlimited Quaternionic Signals
2.3.2 Envelope Detection Using Generalized Analytic Signal in 2D QLCT Domains
2.4 QLCT Related Transforms
2.4.1 Short-Time Special Affine Fourier Transform for Quaternion-Valued Functions
2.4.2 Convolution and Correlation Theorems for Wigner-Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform
2.4.3 Uncertainty Principles for Wigner-Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform
2.4.4 Quaternionic Linear Canonical Wave Packet Transform
3 Other Quaternionic Integral Transforms (QIT)
3.1 Other QIT Theory
3.1.1 On the Quaternionic Short-Time Fourier and Segal-Bargmann Transforms
3.1.2 The Quaternion Fourier Number Transform
3.1.3 The Quaternion Fourier Transform of Finite Measure and Its Properties
3.1.4 The 2-D Hyper-Complex Gabor Quadratic-Phase Fourier Transform and Uncertainty Principles
3.1.5 Monogenic Cauchy Implies Holomorphic Bochner-Martinelli
3.1.6 Boundedness and Uniqueness of Quaternion Weyl Transform
3.1.7 Slice Regular Functions in Several Variables
3.1.8 Bounded Spherical Functions and Heisenberg Inequality on Quaternionic Heisenberg Group
3.2 Other QIT Applications
3.2.1 Two-Sided Fractional Quaternion Fourier Transform and Its Application
3.2.2 Analyzing Real Vector Fields with Clifford Convolution and Clifford-Fourier Transform
3.2.3 Novel Sampling Formulas Associated with Quaternionic Prolate Spheroidal Wave Functions
References
Quaternionic Moments
1 Robust Color Image Watermarking Using Multi-core Raspberry Pi Cluster
2 Helmet-Fourier Orthogonal Moments for Image Representation and Recognition
3 Fast Quaternion Log-polar Radial Harmonic Fourier Moments for Color Image Zero-watermarking
4 New Method for Bio-signals Zero-watermarking Using Quaternion Shmaliy Moments and Short-time Fourier Transform
5 Accurate Quaternion Fractional-order Pseudo-Jacobi-Fourier Moments
References
Octonion Fourier Transform
1 Hypercomplex Fourier Transforms in the Analysis of Multidimensional Linear Time-Invariant Systems
2 Discrete Octonion Fourier Transform and the Analysis of Discrete 3-D Data
3 A Generalization of the Octonion Fourier Transform to 3-D Octonion-Valued Signals: Properties and Possible Applications to 3-D LTI Partial Differential Systems
4 Octonion Fourier Transform of Lipschitz Real-Valued Functions of Three Variables on the Octonion Algebra
5 Octonion Offset Linear Canonical Transform
References

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