| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa |
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2023
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| Descrizione fisica |
1 online resource (XI, 177 p.)
|
| Disciplina |
515.72
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| Collana |
Research Summaries
|
| Soggetto topico |
Mathematical analysis
Fourier analysis
Harmonic analysis
Integral Transforms and Operational Calculus
Fourier Analysis
Abstract Harmonic Analysis
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| ISBN |
3-031-28375-9
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| Formato |
Materiale a stampa  |
| Livello bibliografico |
Monografia |
| Lingua di pubblicazione |
eng
|
| Nota di contenuto |
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.
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| Record Nr. | UNINA-9910736993403321 |
Info
Pseudo-differential operators : 2. ciclo Stresa, 26 agosto-3 settembre 1968 / Centro Internazionale Matematico Estivo ; coordinatore Prof. L. Nirenberg
