Framelets and Wavelets: Algorithms, Analysis, and Applications (Applied and Numerical Harmonic Analysis)

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. Front Matter ....Pages i-xxxiii Discrete Framelet Transforms (Bin Han)....Pages 1-66 Wavelet Filter Banks (Bin Han)....Pages 67-151 Framelet Filter Banks (Bin Han)....Pages 153-244 Analysis of Affine Systems and Dual Framelets (Bin Han)....Pages 245-370 Analysis of Refinable Vector Functions (Bin Han)....Pages 371-483 Framelets and Wavelets Derived from Refinable Functions (Bin Han)....Pages 485-577 Applications of Framelets and Wavelets (Bin Han)....Pages 579-666 Back Matter ....Pages 667-726