## Advances in WaveletsWavelets is a new area that stands at the intersection of the frontiers of mathematics, scientific computing, and signal and image processing, and is one of the major research directions in science in the last decade which is still undergoing rapid growth. This book brings together eleven of the polished versions of the seminars and lectures held over a year-long programme on "Wavelets and their Applications" in Hong Kong, and which cumulated to a workshop in May 1997 which was attended by scientists and graduate students from China, Singapore, North and South America, and Europe. The volume covers the topics of: Theory of frames and applications; Wavelet coefficients; Refinable functions and approximation; Multiwavelets; and Tiling. . Advances in Wavelets will prove a useful reference source to graduate students and researchers alike on the many applications of wavelets. |

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### Contents

Frames Sampling and Seizure Prediction | 1 |

Construction of Compactly Supported Affine | 27 |

Understanding Wavelet Image Coding | 51 |

Copyright | |

6 other sections not shown

### Common terms and phrases

accuracy algebra algorithm Anal approximation order B-spline biorthogonal box spline Chui compactly supported compactly supported distribution compactly supported functions compute conditions of order construction converges Daubechies defined denote digit sets dilation matrix distortion rate dual eigenvalue example exists filter finitely supported Fourier transform fractal Haar Hence implies integer integer translates interpolation Iog2 L2-norm Lemma linearly independent mask Math Mn(Z multiple multiresolution analysis multivariate multiwavelets number of bits orthogonal orthogonal wavelets orthonormal basis P-matrix polynomial Preprint proof proved quantization refinable functions refinement equation result Riesz basis sampling satisfies Condition satisfies the Strang-Fix scalar scaling function scaling vector Section sequence Shen shift-invariant shifts SIAM signal spectral spectral radius Strang-Fix conditions subspace symbol P(z Theorem 4.1 theory tight frame tion transform coding two-scale factor vector of compactly Victor Wickerhauser Wang wavelet bases wavelet coefficients wavelet frames wavelet system zero