Framelets and Wavelets

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.