Wavelets

A. K. Louis and D. Maass are the authors of Wavelets: Theory and Applications, published by Wiley.

• Preface ixNotation xiIntroduction xv1 The Continuous Wavelet Transform 11.1. Definition and Elementary Properties 11.2 Affine Operators 101.3 Filter Properties of the Wavelet Transform 121.4 Approximation Properties 221.5 Decay Behaviour 321.6 Group-Theoretical Foundations and Generalizations 361.7 Extension of the One-Dimensional Wavelet Transform to Sobolev Spaces 59Exercises 692 The Discrete Wavelet Transform 732.1 Wavelet Frames 732.2 Multiscale Analysis 972.3 Fast Wavelet Transform 1212.4 One-Dimensional Orthogonal Wavelets 1312.5 Two-Dimensional Orthogonal Wavelets 203Exercises 2263 Applications of the Wavelet Transform 2313.1 Wavelet Analysis of One-Dimensional Signals 2313.2 Quality Control of Texture 2353.3 Data Compression in Digital Image Processing 2393.4 Regularization of Inverse Problems 2513.5 Wavelet – Galerkin Methods for Two-Point boundary Value Problems 2593.6 Schwarz Iterations Based on Wavelet Decompositions 2783.7 An Outlook on Two-Dimensional Boundary Value Problems 300Exercises 306Appendix The Fourier Transform 309References 313Index 321