An Introduction to Wavelet Analysis

An Introduction to Wavelet Analysis provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases. The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows us to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical pre-requisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts. Features: *Rigorous proofs with consistent assumptions on the mathematical background of the reader; does not assume familiarity with Hilbert spaces or Lebesgue measure * Complete background material on (Fourier Analysis topics) Fourier Analysis * Wavelets are presented first on the continuous domain and later restricted to the discrete domain, for improved motivation and understanding of discrete wavelet transforms and applications. * Special appendix, "Excursions in Wavelet Theory " provides a guide to current literature on the topic * Over 170 exercises guide the reader through the text. The book is an ideal text/reference for a broad audience of advanced students and researchers in applied mathematics, electrical engineering, computational science, and physical sciences. It is also suitable as a self-study reference guide for professionals. All readers will find

Inhaltsverzeichnis

1. Preface, 2. Functions and Convergence, 3. Fourier Series, 4. The Fourier Transform, 5. Signals and Systems, 6. The Haar System, 7. The Discrete Haar Transform, 8. Mulitresolution Analysis, 9. The Discrete Wavelet transform, 10. Smooth, Compactly Supported Wavelets, 11. Biorthogonal Wavelets, 12. Wavelet Packets, 13. Image Compression, 14. Integral Operations; Appendices

Zusammenfassung

An Introduction to Wavelet Analysis provides a comprehensive
presentation
of the conceptual basis of wavelet analysis, including the
construction
and application of wavelet bases. The book develops the basic theory
of wavelet bases and transforms without assuming any knowledge of
Lebesgue integration or the theory of abstract Hilbert spaces. The
book motivates the central ideas of wavelet theory by offering a
detailed exposition of the Haar series, and then shows how a more
abstract approach allows us to generalize and improve upon the Haar
series. Once these ideas have been established and explored,
variations and extensions of Haar construction are presented. The
mathematical pre-requisites for the book are a course in advanced
calculus, familiarity with the language of formal mathematical proofs,
and basic linear algebra concepts. Features: *Rigorous proofs with
consistent assumptions on the mathematical background of the reader;
does not assume familiarity with Hilbert spaces or Lebesgue measure *
Complete background material on (Fourier Analysis topics) Fourier
Analysis * Wavelets are presented first on the continuous domain and
later restricted to the discrete domain, for improved motivation and
understanding of discrete wavelet transforms and applications.
* Special appendix, "Excursions in Wavelet Theory " provides a guide
to
current literature on the topic
* Over 170 exercises guide the reader through the text. The book is
an ideal text/reference for a broad audience of advanced students and
researchers in applied mathematics, electrical engineering,
computational science, and physical sciences. It is also suitable as a
self-study reference guide for professionals. All readers will find

Zusatztext

"[This text] is carefully prepared, well-organized, and covers a large part of the central theory . . . [there are] chapters on biorthogonal wavelets and wavelet packets, topics which are rare in wavelet books. Both are important, and this feature is an extra argument in favour of [this] book . . . the material is accessible [even] to less advanced readers . . . the book is a nice addition to the series."   —Zentralblatt Math

"This book can be recommended to everyone, especially to students looking for a detailed introduction to the subject."   —Mathematical Reviews

"This textbook is an introduction to the mathematical theory of wavelet analysis at the level of advanced calculus. Some applications are described, but the main purpose of the book is to develop—using only tools from a first course in advanced calculus—a solid foundation in wavelet theory. It succeeds admirably. . . . Part I of the book contains 112 pages of preliminary material, consisting of four chapters on ‘Functions and Convergence,’ ‘Fourier Series,’ ‘Fourier Transforms,’ and ‘Signals and Systems.’ . . . This preliminary material is so well written that it could serve as an excellent supplement to a first course in advanced calculus. . . . The heart of the book is Part III: ‘Orthonormal Wavelet bases.’ This material has become the canonical portion of wavelet theory. Walnut does a first-rate job explaining the ideas here. . . . Ample references are supplied to aid the reader. . . . There are exercises at the end of each section, 170 in all, and they seem to be consistent with the level of the text. . . . To cover the whole book would require a year. An excellent one-semester course could be based on a selection of chapters from Parts II, III, and V."   —SIAM Review

"D. Walnut's lovely book aims at the upper undergraduate level, and so it includesrelatively more preliminary material . . . than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform . . . The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended!"   —Bulletin of the AMS

Bericht

"[This text] is carefully prepared, well-organized, and covers a large part of the central theory . . . [there are] chapters on biorthogonal wavelets and wavelet packets, topics which are rare in wavelet books. Both are important, and this feature is an extra argument in favour of [this] book . . . the material is accessible [even] to less advanced readers . . . the book is a nice addition to the series."   -Zentralblatt Math
"This book can be recommended to everyone, especially to students looking for a detailed introduction to the subject."   -Mathematical Reviews
"This textbook is an introduction to the mathematical theory of wavelet analysis at the level of advanced calculus. Some applications are described, but the main purpose of the book is to develop-using only tools from a first course in advanced calculus-a solid foundation in wavelet theory. It succeeds admirably. . . . Part I of the book contains 112 pages of preliminary material, consisting of four chapters on 'Functions and Convergence,' 'Fourier Series,' 'Fourier Transforms,' and 'Signals and Systems.' . . . This preliminary material is so well written that it could serve as an excellent supplement to a first course in advanced calculus. . . . The heart of the book is Part III: 'Orthonormal Wavelet bases.' This material has become the canonical portion of wavelet theory. Walnut does a first-rate job explaining the ideas here. . . . Ample references are supplied to aid the reader. . . . There are exercises at the end of each section, 170 in all, and they seem to be consistent with the level of the text. . . . To cover the whole book would require a year. An excellent one-semester course could be based on a selection of chapters from Parts II, III, and V."   -SIAM Review
"D. Walnut's lovely book aims at the upper undergraduate level, and so it includesrelatively more preliminary material . . . than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform . . . The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended!"   -Bulletin of the AMS

Produktdetails

• Autoren: David F Walnut, David F. Walnut
• Verlag: Springer, Basel
• Sprache: Englisch
• Produktform: Taschenbuch
• Erschienen: 22.04.2014
• EAN: 9781461265672
• ISBN: 978-1-4612-6567-2
• Seiten: 452
• Abmessung: 155 mm x 236 mm x 26 mm
• Gewicht: 718 g
• Illustration: XX, 452 p.
• Serien: Applied and Numerical Harmonic Analysis; Applied and Numerical Harmonic Analysis
• Themen: Naturwissenschaften, Medizin, Informatik, Technik > Informatik, EDV > Allgemeines, Lexika; A, Mathematics and Statistics, Applications of Mathematics, Functional Analysis, Signal, Image and Speech Processing, Computational Mathematics and Numerical Analysis, Signal Processing, Computer mathematics, Numerical analysis, Engineering mathematics, Applied mathematics, Computational Science and Engineering, Speech processing systems, Imaging systems & technology, Image processing, Functional analysis & transforms, Signal, Speech and Image Processing