**Author**: Todd Ogden

**Publisher:** Springer Science & Business Media

**ISBN:** 9780817638641

**Category : **Mathematics

**Languages : **en

**Pages : **206

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**Book Description**
I once heard the book by Meyer (1993) described as a "vulgarization" of wavelets. While this is true in one sense of the word, that of making a sub ject popular (Meyer's book is one of the early works written with the non specialist in mind), the implication seems to be that such an attempt some how cheapens or coarsens the subject. I have to disagree that popularity goes hand-in-hand with debasement. is certainly a beautiful theory underlying wavelet analysis, there is While there plenty of beauty left over for the applications of wavelet methods. This book is also written for the non-specialist, and therefore its main thrust is toward wavelet applications. Enough theory is given to help the reader gain a basic understanding of how wavelets work in practice, but much of the theory can be presented using only a basic level of mathematics. Only one theorem is for mally stated in this book, with only one proof. And these are only included to introduce some key concepts in a natural way.

**Author**: Todd Ogden

**Publisher:** Springer Science & Business Media

**ISBN:** 9780817638641

**Category : **Mathematics

**Languages : **en

**Pages : **206

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**Book Description**
I once heard the book by Meyer (1993) described as a "vulgarization" of wavelets. While this is true in one sense of the word, that of making a sub ject popular (Meyer's book is one of the early works written with the non specialist in mind), the implication seems to be that such an attempt some how cheapens or coarsens the subject. I have to disagree that popularity goes hand-in-hand with debasement. is certainly a beautiful theory underlying wavelet analysis, there is While there plenty of beauty left over for the applications of wavelet methods. This book is also written for the non-specialist, and therefore its main thrust is toward wavelet applications. Enough theory is given to help the reader gain a basic understanding of how wavelets work in practice, but much of the theory can be presented using only a basic level of mathematics. Only one theorem is for mally stated in this book, with only one proof. And these are only included to introduce some key concepts in a natural way.

**Author**: Eric J. Stollnitz

**Publisher:** Morgan Kaufmann

**ISBN:** 9781558603752

**Category : **Computers

**Languages : **en

**Pages : **245

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**Book Description**
This distinctly accessible introduction to wavelets provides computer graphics professionals and researchers with the mathematical foundations for understanding and applying this powerful tool. Wavelets are rapidly becoming a core technique in computer graphics, with applications for Image editing and compression Automatic level-of-detail control for editing and rendering curves and surfaces Surface reconstruction from contours Physical simulation for global illumination and animation Stressing intuition and clarity, this book offers a solid understanding of the theory of wavelets and their proven applications in computer graphics. Although previous introductions to wavelets have presented an elegant mathematical framework, that framework is too restrictive to apply to many problems in graphics. In contrast, this book focuses on a generalized theory that naturally accommodates the kinds of objects that commonly arise in computer graphics, including images, open curves, and surfaces of arbitrary topology. This book also contains a foreword by Ingrid Daubechies and an appendix covering the necessary background material in linear algebra.

**Author**: Yves Nievergelt

**Publisher:** Springer Science & Business Media

**ISBN:** 9780817640613

**Category : **Mathematics

**Languages : **en

**Pages : **297

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**Book Description**
This book, written at the level of a first course in calculus and linear algebra, offers a lucid and concise explanation of mathematical wavelets. Evolving from ten years of classroom use, its accessible presentation is designed for undergraduates in a variety of disciplines (computer science, engineering, mathematics, mathematical sciences) as well as for practising professionals in these areas. This unique text starts the first chapter with a description of the key features and applications of wavelets, focusing on Haar's wavelets but using only high school mathematics. The next two chapters introduce one-, two-, and three-dimensional wavelets, with only the occasional use of matrix algebra. The second part of this book provides the foundations of least squares approximation, the discrete Fourier transform, and Fourier series. The third part explains the Fourier transform and then demonstrates how to apply basic Fourier analysis to designing and analyzing mathematical wavelets. Particular attention is paid to Daubechies wavelets. Numerous exercises, a bibliography, and a comprehensive index combine to make this book an excellent text for the classroom as well as a valuable resource for self-study.

**Author**: P. Wojtaszczyk

**Publisher:** Cambridge University Press

**ISBN:** 9780521578943

**Category : **Mathematics

**Languages : **en

**Pages : **261

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**Book Description**
The only introduction to wavelets that doesn't avoid the tough mathematical questions.

**Author**: Stephane Jaffard

**Publisher:** SIAM

**ISBN:** 9780898718119

**Category : **Electronic books

**Languages : **en

**Pages : **269

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**Book Description**
This long-awaited update of Meyer's Wavelets : algorithms and applications includes completely new chapters on four topics: wavelets and the study of turbulence, wavelets and fractals (which includes an analysis of Riemann's nondifferentiable function), data compression, and wavelets in astronomy. The chapter on data compression was the original motivation for this revised edition, and it contains up-to-date information on the interplay between wavelets and nonlinear approximation. The other chapters have been rewritten with comments, references, historical notes, and new material. Four appendices have been added: a primer on filters, key results (with proofs) about the wavelet transform, a complete discussion of a counterexample to the Marr-Mallat conjecture on zero-crossings, and a brief introduction to Hölder and Besov spaces. In addition, all of the figures have been redrawn, and the references have been expanded to a comprehensive list of over 260 entries. The book includes several new results that have not appeared elsewhere.

**Author**: Jean-Michel Combes

**Publisher:** Springer Science & Business Media

**ISBN:** 3642759882

**Category : **Science

**Languages : **en

**Pages : **331

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**Book Description**
The last two subjects mentioned in the title "Wavelets, Time Frequency Methods and Phase Space" are so well established that they do not need any explanations. The first is related to them, but a short introduction is appropriate since the concept of wavelets emerged fairly recently. Roughly speaking, a wavelet decomposition is an expansion of an arbitrary function into smooth localized contributions labeled by a scale and a position pa rameter. Many of the ideas and techniques related to such expansions have existed for a long time and are widely used in mathematical analysis, theoretical physics and engineering. However, the rate of progress increased significantly when it was realized that these ideas could give rise to straightforward calculational methods applicable to different fields. The interdisciplinary structure (R.C.P. "Ondelettes") of the C.N.R.S. and help from the Societe Nationale Elf-Aquitaine greatly fostered these developments. The conference, the proceedings of which are contained in this volume, was held at the Centre National de Rencontres Mathematiques (C.N.R.M) in Marseille from December 14-18, 1987 and bought together an interdisciplinary mix of par ticipants. We hope that these proceedings will convey to the reader some of the excitement and flavor of the meeting.

**Author**: John J. Benedetto

**Publisher:** CRC Press

**ISBN:** 1000443469

**Category : **Mathematics

**Languages : **en

**Pages : **592

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**Book Description**
Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented. The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.

**Author**: Gordon Erlebacher

**Publisher:** Oxford University Press on Demand

**ISBN:** 0195094239

**Category : **History

**Languages : **en

**Pages : **510

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**Book Description**
Wavelets are spatially localized functions whose amplitude drops off exponentially outside a small "window." They are used to magnify experimental or numerical data and have become powerful tools in signal processing and other computational sciences. This book gives scientists and engineers a practical understanding of wavelets--their origins, their purpose, their use, and their prospects. It covers the applications of wavelets as a diagnostic tool and the use of wavelet basis functions to solve differential equations. Each chapter was written by one of five lecturers of a course sponsored by the Institute of Computer Applications in Science and Engineering (ICASE) and the NASA Langley Research Center. Not only does this book treat the latest advances on the subject, but it also attempts to impart practical knowledge to allow scientists and engineers to evaluate objectively where these tools stand in relation to their needs.

**Author**: G Battle

**Publisher:** World Scientific

**ISBN:** 9814499129

**Category : **Mathematics

**Languages : **en

**Pages : **580

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**Book Description**
WAVELETS AND RENORMALIZATION describes the role played by wavelets in Euclidean field theory and classical statistical mechanics. The author begins with a stream-lined introduction to quantum field theory from a rather basic point of view. Functional integrals for imaginary-time-ordered expectations are introduced early and naturally, while the connection with the statistical mechanics of classical spin systems is introduced in a later chapter. A vastly simplified (wavelet) version of the celebrated Glimm-Jaffe construction of the Φ43 quantum field theory is presented. It is due to Battle and Federbush, and it bases an inductively defined cluster expansion on a wavelet decomposition of the Euclidean quantum field. The presentation is reserved for the last chapter, while the more basic aspects of cluster expansions are reviewed in the chapter on classical spin systems. Wavelets themselves are studied from two different points of view arising from two disciplines. The mathematical point of view covers the basic properties of wavelets and methods for constructing well-known wavelets such as Meyer wavelets, Daubechies wavelets, etc. The physical point of view covers the renormalization group formalism, where there is a close connection between wavelets and Gaussian fixed points. The book is heavily mathematical, but avoids the theorem-proof-theorem-proof format in the interests of preserving the flow of the discussion — i.e., it is written in the style of an old-fashioned theoretical physics book, but the major claims are rigorously proven. The minor themes of the book are reflection positivity, the combinatorics of cluster expansions, and the issue of phase transitions — themes which have nothing to do with wavelets, but which provide necessary cultural background for the physical context. Contents:Mathematical Sketches of Quantum PhysicsWavelets — Basic Theory and ConstructionEquilibrium States of Classical CrystalsA Wavelet Introduction to the Renormalization GroupWavelet Analysis of Φ43 Readership: Applied mathematicians. keywords:Cluster Expansions;Condensed Matter;Euclidean Fields;Functional Integrals;Phase Space;Quantum Mechanics;Reflection Positivity;Renormalization Group;Uncertainty Principle;Wavelets “… the author has succeeded in giving a vivid and pedagogical presentation of a monumental work in recent mathematical physics, illustrating the mutual influence between wavelet analysis and renormalization group techniques of Euclidean field theory.” Mathematical Reviews “This book is a great achievement. It is difficult to read, but very rewarding for those who read it in depth.” Monatshefte für Mathematik

**Author**: Barbara Burke Hubbard

**Publisher:** CRC Press

**ISBN:** 1439864551

**Category : **Mathematics

**Languages : **en

**Pages : **286

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**Book Description**
This best-selling book introduces a broad audience including scientists and engineers working in a variety of fields as well as mathematicians from other subspecialties to one of the most active new areas of applied mathematics and the story of its discovery and development. Organized in "hypertext fashion," the book tells a story of scientific discovery with separate brief entries for technical terms and explicit appendices in a section called "Beyond Plain English."