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Birkhäuser

Wavelet Analysis and Applications

  • Conference proceedings
  • © 2007

Overview

Editors:
  1. Tao Qian

    1. Faculty of Science and Technology, University of Macau, Macau

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  2. Mang I Vai

    1. Faculty of Science and Technology, University of Macau, Macau

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  3. Yuesheng Xu

    1. Department of Mathematics, Syracuse University, Syracuse, USA

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  • Based on the conference Wavelet Analysis and Applications 2005 held November 29 -December 2, at the University of Macau
  • Contains carefully selected and rigorously reviewed contributions giving a good picture of the state of the art in wavelet analysis and its manifold applications
  • Includes supplementary material: sn.pub/extras

Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)

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Table of contents (41 papers)

  1. Front Matter

    Pages i-xiv
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  2. Wavelet Theory

    1. Front Matter

      Pages 1-1
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    3. Construction of Wavelets and Frame Theory

      1. Orthogonal Wavelet Vectors in a Hilbert Space
        • Huai-Xin Cao, Bao-Min Yu
        Pages 59-66
      2. Operator Frames for <span class="mathjax-tex">\( B(\mathcal{H}) \)</span>
        • Chun-Yan Li, Huai-Xin Cao
        Pages 67-82
      3. On the Stability of Multi-wavelet Frames
        • Gang Wang, ZhengXing Cheng
        Pages 83-90
      4. Biorthogonal Wavelets Associated with Two-Dimensional Interpolatory Function
        • Jianwei Yang, Yuan Yan Tang, Zhengxing Cheng, Xinge You
        Pages 91-98
      5. Parameterization of Orthogonal Filter Bank with Linear Phase
        • Xiaoxia Feng, Zhengxing Cheng, Zhongpeng Yang
        Pages 99-106
      6. On Multivariate Wavelets with Trigonometric Vanishing Moments
        • Ying Li, Zhi-Dong Deng, Yan-Chun Liang
        Pages 107-121
      7. Directional Wavelet Analysis with Fourier-Type Bases for Image Processing
        • Zhen Yao, Nasir Rajpoot, Roland Wilson
        Pages 123-142
      8. Unitary Systems and Wavelet Sets
        • David R. Larson
        Pages 143-171
      9. Clifford Analysis and the Continuous Spherical Wavelet Transform
        • Paula Cerejeiras, Milton Ferreira, Uwe Kähler
        Pages 173-184
      10. Clifford-Jacobi Polynomials and the Associated Continuous Wavelet Transform in Euclidean Space
        • Fred Brackx, Nele De Schepper, Frank Sommen
        Pages 185-198

    4. Fractal and Multifractal Theory, Wavelet Algorithm, Wavelet in Numerical Analysis

      1. Wavelet Leaders in Multifractal Analysis
        • Stéphane Jaffard, Bruno Lashermes, Patrice Abry
        Pages 201-246
      2. Application of Fast Wavelet Transformation in Parametric System Identification
        • Klaus Markwardt
        Pages 247-254
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Keywords

About this book

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.

Editors and Affiliations

  • Faculty of Science and Technology, University of Macau, Macau

    Tao Qian, Mang I Vai

  • Department of Mathematics, Syracuse University, Syracuse, USA

    Yuesheng Xu

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