Mathematical Methods in Time Series Analysis and Digital Image Processing (Understanding Complex Systems)
~ Dahlhaus R., et al. (eds.)
Details
# Hardcover: 294 pages
# Publisher: Springer; 1 edition (February 25, 2008)
# Language: English
# ISBN-10: 3540756310
# ISBN-13: 978-3540756316
Description
The aim of this volume is to bring together research directions in theoretical signal and imaging processing developed rather independently in electrical engineering, theoretical physics, mathematics and the computer sciences.
In particular, mathematically justified algorithms and methods, the mathematical analysis of these algorithms, and methods as well as the investigation of connections between methods from time series analysis and image processing are reviewed. An interdisciplinary comparison of these methods, drawing upon common sets of test problems from medicine and geophysical/environmental sciences, is also addressed.
This volume coherently summarizes work carried out in the field of theoretical signal and image processing. It focuses on non-linear and non-parametric models for time series as well as on adaptive methods in image processing.
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A Mathematical Introduction to Wavelets (London Mathematical Society Student Texts)
by: P. Wojtaszczyk
Details
# Paperback: 276 pages
# Publisher: Cambridge University Press (February 13, 1997)
# Language: English
# ISBN-10: 0521578949
# ISBN-13: 978-0521578943
Description
This book presents a mathematical introduction to the theory of orthogonal wavelets and their uses in analyzing functions and function spaces, both in one and in several variables. Starting with a detailed and self-contained discussion of the general construction of one dimensional wavelets from multiresolution analysis, the book presents in detail the most important wavelets: spline wavelets, Meyer's wavelets and wavelets with compact support. It then moves to the corresponding multivariable theory and gives genuine multivariable examples. The author discusses wavelet decompositions in Lp spaces, Hardy spaces and Besov spaces and provides wavelet characterizations of those spaces. Also included are periodic wavelets or wavelets not associated with a multiresolution analysis. This will be an invaluable book for those wishing to learn about the mathematical foundations of wavelets.
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First Course in Wavelets with Fourier Analysis
by: Albert Boggess Francis J. Narcowich
Details
# Hardcover: 315 pages
# Publisher: Wiley; 2 edition (September 8, 2009)
# Language: English
# ISBN-10: 0470431172
# ISBN-13: 978-0470431177
Description
A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition
Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level.
The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature:
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The development of a Fourier series, Fourier transform, and discrete Fourier analysis
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Improved sections devoted to continuous wavelets and two-dimensional wavelets
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The analysis of Haar, Shannon, and linear spline wavelets
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The general theory of multi-resolution analysis
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Updated MATLAB® code and expanded applications to signal processing
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The construction, smoothness, and computation of Daubechies' wavelets
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Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform
Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB® routines that supplement the presented examples.
A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.
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Approximation Theory: From Taylor Polynomials to Wavelets (Applied and Numerical Harmonic Analysis)
by: Ole Christensen Khadija L. Christensen
Details
# Paperback: 165 pages
# Publisher: Birkhäuser Boston (September 20, 2005)
# Language: English
# ISBN-10: 0817636005
# ISBN-13: 978-0817636005
Description
This concisely written book gives an elementary introduction to a classical area of mathematics---approximation theory---in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications.
Key features and topics:
* Description of wavelets in words rather than mathematical symbols * Elementary introduction to approximation using polynomials (Weierstrass' and Taylor's theorems) * Introduction to infinite series, with emphasis on approximation-theoretic aspects * Introduction to Fourier analysis * Numerous classical, illustrative examples and constructions * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI's use of wavelets to store fingerprints * Minimal prerequisites: elementary calculus * Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series
"Approximation Theory: From Taylor Polynomials" to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas.
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