# Framelets and Wavelets

## Algorithms, Analysis, and Applications

• Bin Han
Textbook

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

1. Front Matter
Pages i-xxxiii
2. Bin Han
Pages 1-66
3. Bin Han
Pages 67-151
4. Bin Han
Pages 153-244
5. Bin Han
Pages 245-370
6. Bin Han
Pages 371-483
7. Bin Han
Pages 485-577
8. Bin Han
Pages 579-666
9. Back Matter
Pages 667-726

### Introduction

Marking a distinct departure from the perspectives of frame theory and discrete transforms, this book provides a comprehensive mathematical and algorithmic introduction to wavelet theory. As such, it can be used as either a textbook or reference guide.

As a textbook for graduate mathematics students and beginning researchers, it offers detailed information on the basic theory of framelets and wavelets, complemented by self-contained elementary proofs, illustrative examples/figures, and supplementary exercises.

Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwavelets/multiframelets in Sobolev spaces and directional framelets) in wavelet theory, together with systematic mathematical analysis, concrete algorithms, and recent developments in and applications of framelets and wavelets.

Lastly, the book can also be used to teach on or study selected special topics in approximation theory, Fourier analysis, applied harmonic analysis, functional analysis, and wavelet-based signal/image processing.

### Keywords

framelets and wavelets discrete framalet/wavelet transform orthogonal and biorthogonal wavelets tight and dual framelets wavelet and framelet filter banks nonhomogeneous and homogeneous affine systems refinable structure refinable vector functions mulitframelets and multiwavelets refinable splines linear independence and stability cascade algorithms and subdivision schemes sum rules vanishing moments linear-phase moments approximation order quasi-approximation operators shift-invariant spaces multiresolution analysis

#### Authors and affiliations

• Bin Han
• 1
1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada