Qian / Xu Wavelet Analysis and Applications

1. Auflage 2007
ISBN: 978-3-7643-7778-6
Verlag: Springer
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 574 Seiten

This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often been said to be mainly an applied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics. Key topics: Approximation and Fourier Analysis Construction of Wavelets and Frame Theory Fractal and Multifractal Theory Wavelets in Numerical Analysis Time-Frequency Analysis Adaptive Representation of Nonlinear and Non-stationary Signals Applications, particularly in image processing Through the broad spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike.

Autoren/Hrsg.

Qian, Tao

Xu, Yuesheng

Inhaltsverzeichnis

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