Framelets and Wavelets
Description
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.
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Person
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.
Content
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.