This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. Wavelets are a mathematical development that many experts think may revolutionize the world of information storage and retrieval. They are a fairly simple mathematical tool now being applied to the compression of data, such as fingerprints, weather satellite photographs, and medical x-rays - that were previously thought to be impossible to condense without losing crucial details. The opening chapter provides an overview of the main problems presented in the book. Following chapters discuss the theoretical and practical aspects of wavelet theory, including wavelet transforms, orthonormal bases of wavelets, and characterization of functional spaces by means of wavelets. The last chapter presents several topics under active research, as multidimensional wavelets, wavelet packet bases, and a construction of wavelets tailored to decompose functions defined in a finite interval.
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Editorial Reviews
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‘This is a marvellous book written by one of the principal contributors to the field. … a great part of the volume under review is dedicated to the engineering and physical origins of wavelets. … The book style is alert and the interest of the potential reader is continuously kept alive. I think that this book is very useful to mathematicians as well as to people interested in the wavelets applications (engineers, physicists, etc.).’ Nicolae Popa, Romanian Journal of Pure and Applied Mathematics
‘Ingrid Daubechies is a leading wavelet theorist; this book gives a clear and systematic treatment of the mathematics. Applications are kept in mind all the time, but the main focus of attention is a rigorous development of the theory. … The book is carefully written; proofs are given in detail for the benefit of non-expert readers yet there is plenty of broad-brush explanation to balance the rigorous mathematical detail.’ D. H. Griffel, The Mathematical Gazette
‘ … this is a clearly written introduction to the mathematics of wavelets that provides solid background material on most of the major aspects of the current theory. Especially appealing is the way in which the relationships between wavelets and other areas are pointed out. … I feel certain that this will be the major introductory text on wavelets for some time to come. It will definitely be a welcome addition to the library of anyone interested in learning the basics of wavelets.’ Christopher Heil, SIAM Review
‘This book is both a tutorial on wavelets and a review of the most advanced research in this domain … it also gives many practical examples and describes several applications (in particular, in signal processing, image coding and numerical analysis).’ Mathematical Reviews
‘ … I heartily recommend this book to anyone who seriously wants to know the state of the art in wavelets. The modest … is a real bargain for the wealth of information it contains … I have changed from one who is skeptical because of wavelets being fashionable to one who has the opinion that wavelets are here to stay and will become a standard tool in many applications. This book is likely to become a classic text in mathematics and a reference to those seriously using wavelets. It is exciting to read a soon-to-be classic.’ Journal of Electronic Imaging
"The book by Daubechies, who is one of the main developers of the (wavelet) theory, is the result of an intensive short course. The presentation is completely engrossing; it is like reading a good, thick Russian novel. Daubechies has a real knack for making the material appealing and lively, and there is a definite 'slowing down for details' at the points that require further elucidation. …This book can be used for many different purposes, from individual reading to graduate-level course-work, and it will likely become a classic." -- F. Alberto Grünbaum, Science, August 7, 1992.
‘Ingrid Daubechies is a leading wavelet theorist; this book gives a clear and systematic treatment of the mathematics. Applications are kept in mind all the time, but the main focus of attention is a rigorous development of the theory. … The book is carefully written; proofs are given in detail for the benefit of non-expert readers yet there is plenty of broad-brush explanation to balance the rigorous mathematical detail.’ D. H. Griffel, The Mathematical Gazette
‘ … this is a clearly written introduction to the mathematics of wavelets that provides solid background material on most of the major aspects of the current theory. Especially appealing is the way in which the relationships between wavelets and other areas are pointed out. … I feel certain that this will be the major introductory text on wavelets for some time to come. It will definitely be a welcome addition to the library of anyone interested in learning the basics of wavelets.’ Christopher Heil, SIAM Review
‘This book is both a tutorial on wavelets and a review of the most advanced research in this domain … it also gives many practical examples and describes several applications (in particular, in signal processing, image coding and numerical analysis).’ Mathematical Reviews
‘ … I heartily recommend this book to anyone who seriously wants to know the state of the art in wavelets. The modest … is a real bargain for the wealth of information it contains … I have changed from one who is skeptical because of wavelets being fashionable to one who has the opinion that wavelets are here to stay and will become a standard tool in many applications. This book is likely to become a classic text in mathematics and a reference to those seriously using wavelets. It is exciting to read a soon-to-be classic.’ Journal of Electronic Imaging
"The book by Daubechies, who is one of the main developers of the (wavelet) theory, is the result of an intensive short course. The presentation is completely engrossing; it is like reading a good, thick Russian novel. Daubechies has a real knack for making the material appealing and lively, and there is a definite 'slowing down for details' at the points that require further elucidation. …This book can be used for many different purposes, from individual reading to graduate-level course-work, and it will likely become a classic." -- F. Alberto Grünbaum, Science, August 7, 1992.
Book Description
This monograph contains 10 lectures presented by Dr. Daubechies at the 1990 CBMS-NSF Conference on Wavelets and Applications. The opening chapter outlines the main problems presented in the book; following chapters discuss the theoretical and practical aspects of wavelet theory, whilst the last chapter presents several topics under active research.
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Most Helpful Customer Reviews
14 of 17 people found the following review helpful:
3.0 out of 5 stars
Theoretical Wonder....but you won't learn wavelets from it!,
By A Customer
This review is from: Ten Lectures on Wavelets (CBMS-NSF Regional Conference Series in Applied Mathematics) (Paperback)
This is the document that started it all. It is by far a great mathematical and theoritical piece of work. HOWEVER, if you are just starting off and want to learn about wavelets and do not have an advanced math or engineering degree (and I do mean ADVANCED), do not pick up this book. At least not at the beginning. There are much better books written for explaining wavelets and to better present the material. Ten Lectures is essentially one big proof. Try Mallat/Kovacevic or Strang...once you've got a solid understanding, come back to Daubechies and marvel at her work.
7 of 8 people found the following review helpful:
5.0 out of 5 stars
Great for everyone!,
By Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews (VINE VOICE) (REAL NAME)
This review is from: Ten Lectures on Wavelets (CBMS-NSF Regional Conference Series in Applied Mathematics) (Paperback)
This book has become a classic,-- and a hit;-- for more than ten reasons. It is multilayered, and yet presents a unity of ideas: The material, and the writing is engaging for the beginner, and for the research mathematician alike. When I used it in my teaching, it was equally popular with the math students, and those from engineering. I don't know if I can say this about any other book I have taught from. The students could follow all the carefully presented proofs, and the engineer could generate algorithms from the applied chapters.
5 of 7 people found the following review helpful:
4.0 out of 5 stars
Not for the faint of heart!,
By A Customer
This review is from: Ten Lectures on Wavelets (CBMS-NSF Regional Conference Series in Applied Mathematics) (Paperback)
This book is a treasure of details if you know what you are doing. As another reviewer noted, it is not for the beginner. But if you have had some experience with the subject this is a must have for your library shelf.
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First Sentence:
This preliminary chapter fixes notation conventions and normalizations. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bargmann Hilbert New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This preliminary chapter fixes notation conventions and normalizations. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bargmann Hilbert New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 48
books:
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100
books
cite this book:
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- Multirate Systems And Filter Banks by P. P. Vaidyanathan on page 2, and Back Matter
- Robust Statistical Procedures (CBMS-NSF Regional Conference Series in Applied Mathematics) by Peter J. Huber in Front Matter, and Back Matter
- Wavelets, Volume 2: A Tutorial in Theory and Applications (Wavelet Analysis and Its Applications) by Charles K. Chui on page 2, and Back Matter
- Variational Methods for Eigenvalue Approximation (CBMS-NSF Regional Conference Series in Applied Mathematics) by Hans F. Weinberger in Front Matter
- Special Functions (Encyclopedia of Mathematics and its Applications) by George E. Andrews in Front Matter
See all 48 books this book cites
- Wavelets in Medicine and Biology by Akram Aldroubi on 9 pages
- Advances in Gabor Analysis by Hans G. Feichtinger on 7 pages
- Wavelets in Electromagnetics and Device Modeling (Wiley Series in Microwave and Optical Engineering) by George W. Pan on 6 pages
- Multiscale and Multiresolution Methods: Theory and Applications (Lecture Notes in Computational Science and Engineering) by Timothy J. Barth on 4 pages
- Operator Theory, Operator Algebras, and Applications (Contemporary Mathematics) by Palle E. T. Jorgensen, and David Royal Larson Deguang Han on 4 pages
See all 100 books citing this book
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