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.
