Wavelet Analysis and Applications

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.

Wavelet Theory.- Local Smoothness Conditions on a Function Which Guarantee Convergence of Double Walsh-Fourier Series of This Function.- Linear Transformations of ?N and Problems of Convergence of Fourier Series of Functions Which Equal Zero on Some Set.- Sidon Type Inequalities for Wavelets.- Almansi Decomposition for Dunkl-Helmholtz Operators.- An Uncertainty Principle for Operators.- Uncertainty Principle for Clifford Geometric Algebras Cl n,0, n = 3 (mod 4) Based on Clifford Fourier Transform.- Orthogonal Wavelet Vectors in a Hilbert Space.- Operator Frames for .- On the Stability of Multi-wavelet Frames.- Biorthogonal Wavelets Associated with Two-Dimensional Interpolatory Function.- Parameterization of Orthogonal Filter Bank with Linear Phase.- On Multivariate Wavelets with Trigonometric Vanishing Moments.- Directional Wavelet Analysis with Fourier-Type Bases for Image Processing.- Unitary Systems and Wavelet Sets.- Clifford Analysis and the Continuous Spherical Wavelet Transform.- Clifford-Jacobi Polynomials and the Associated Continuous Wavelet Transform in Euclidean Space.- Wavelet Leaders in Multifractal Analysis.- Application of Fast Wavelet Transformation in Parametric System Identification.- Image Denoising by a Novel Digital Curvelet Reconstruction Algorithm.- Condition Number for Under-Determined Toeplitz Systems.- Powell-Sabin Spline Prewavelets on the Hexagonal Lattice.- Time-Frequency Aspects of Nonlinear Fourier Atoms.- Mono-components for Signal Decomposition.- Signal-Adaptive Aeroelastic Flight Data Analysis with HHT.- An Adaptive Data Analysis Method for Nonlinear and Nonstationary Time Series: The Empirical Mode Decomposition and Hilbert Spectral Analysis.- Wavelet Applications.- Transfer Colors from CVHD to MRI Based on Wavelets Transform.-Medical Image Fusion by Multi-resolution Analysis of Wavelets Transform.- Salient Building Detection from a Single Nature Image via Wavelet Decomposition.- SAR Images Despeckling via Bayesian Fuzzy Shrinkage Based on Stationary Wavelet Transform.- Super-Resolution Reconstruction Using Haar Wavelet Estimation.- The Design of Hilbert Transform Pairs in Dual-Tree Complex Wavelet Transform.- Supervised Learning Using Characteristic Generalized Gaussian Density and Its Application to Chinese Materia Medica Identification.- A Novel Algorithm of Singular Points Detection for Fingerprint Images.- Wavelet Receiver: A New Receiver Scheme for Doubly-Selective Channels.- Face Retrieval with Relevance Feedback Using Lifting Wavelets Features.- High-Resolution Image Reconstruction Using Wavelet Lifting Scheme.- Mulitiresolution Spatial Data Compression Using Lifting Scheme.- Ridgelet Transform as a Feature Extraction Method in Remote Sensing Image Recognition.- Analysis of Frequency Spectrum for Geometric Modeling in Digital Geometry.- Detection of Spindles in Sleep EEGs Using a Novel Algorithm Based on the Hilbert-Huang Transform.- A Wavelet-Domain Hidden Markov Tree Model with Localized Parameters for Image Denoising.