Wavelet Analysis and Applications (eBook)

Preface 7
Contents 11
Part 1. Wavelet Theory 15
Local Smoothness Conditions on a Function Which Guarantee Convergence of Double Walsh-Fourier Series of This Function 17
Linear Transformations of Rn and Problems of Convergence of Fourier Series of Functions Which Equal Zero on Some Set 26
Sidon Type Inequalities for Wavelets 38
Almansi Decomposition for Dunkl-Helmholtz Operators 47
An Uncertainty Principle for Operators 55
Uncertainty Principle for Clifford Geometric Algebras 59
Orthogonal Wavelet Vectors in a Hilbert Space 70
Operator Frames for B(H) 78
On the Stability of Multi-wavelet Frames 94
Biorthogonal Wavelets Assocoated with Two-Dimensional Interpolatory Function 102
Parameterization of Orthogonal Filter Bank with Linear Phase 110
On Multivariate Wavelets with Trigonometric Vanishing Moments 118
Directional Wavelet Analysis with Fourier-Type Bases for Image Processing 133
Unitary Systems and Wavelet Sets 153
Clifford Analysis and the Continuous Spherical Wavelet Transform 182
Clifford-Jacobi Polynomials and the Associated Continuous Wavelet Transform in Euclidean Space 194
Wavelet Leaders in Multifractal Analysis 209
Application of Fast Wavelet Transformation in Parametric System Identification 255
Image Denoising by a Novel Digital Curvelet Reconstruction Algorithm 263
Condition Number for Under-Determined Toeplitz Systems 270
Powell-Sabin Spline Prewavelets on the Hexagonal Lattice 279
Time-Frequency Aspects of Nonlinear Fourier Atoms 291
Mono-components for Signal Decomposition 302
Signal-Adaptive Aeroelastic Flight Data Analysis with HHT 323
An Adaptive Data Analysis Method for Nonlinear and Nonstationary Time Series 365
Part 2. Wavelet Applications 379
Transfer Colors form CVHD to MRI Based on Wavelets Transform 382
Medical Image Fusion by Multi-resolution Analysis of Wavelets Transform 390
Salient Building Detection from a Single Nature image via Wavelet Decomposition 398
SAR Images Despeckling 407
Super-Resolution Reconstruction Using Haar Wavelet Estimation 418
The Design of Hilbert Transform Pairs in Dual-Tree Complex Wavelet Transform 430
Supervised Learning Using Characteristic Generalized Gaussian Density and Its Application to Chinese Materia Medica Identification 441
A Novel Algorithm of Singular Points Detection for Fingerprint Images 451
Wavelet Receiver: A New Receiver Scheme for Doubly Selective Channels 461
Face Retrieval with Relevance Feedback Using Lifting Wavelets Features 474
High-Resolution Image Reconstruction Using Wavelet Lifting Scheme 485
Multiresolution Spatial Data Compression Using Lifting Scheme 499
Ridgelet Transformation as a Feature extraction Method in Remote Sensing Image Regognition 510
Analysis of Frequency Spectrum for Geometric Medeling in Digital Geometry 519
Detection of Spindles in Sleep EEGs 537
A Wavelet-Domain Hidden Markov Tree Model with Localized Parameters for Image Denoising 554