Description
Framelets and Wavelets, Softcover reprint of the original 1st ed. 2017
Algorithms, Analysis, and Applications
Applied and Numerical Harmonic Analysis Series
Author: Han Bin
Language: English
Subject for Framelets and Wavelets:
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
Publication date: 06-2019
724 p. · 15.5x23.5 cm · Paperback
Publication date: 01-2018
Support: Print on demand
Description
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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.
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.
Preface.- Chapter 1. Discrete Framelet Transforms.- Chapter 2. Wavelet Filter Banks.- Chapter 3. Framelet Filter Banks.- Chapter 4. Analysis of Affine Systems and Dual Framelets.- Chapter 5. Analysis of Refinable Vector Functions.- Chapter 6. Framelets and Wavelets Derived from Refinable Functions.- Chapter 7. Applications of Framelets and Wavelets.- Appendix A. Basics on Fourier Analysis.- Notes and Acknowledgments.- Bibliography.- Index.
Bin Han been working in the area of applied harmonic analysis and approximation theory, in particular, on wavelets and framelets with applications since 1992. He received his PhD in mathematics at the University of Alberta in 1998 and worked as a PDF at Princeton University in 1999. Bin Han is professor of mathematics at the University of Alberta.
