Four Short Courses on Harmonic Analysis
Wavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis
Forster, Brigitte.
editor.
Massopust, Peter.
editor.
SpringerLink (Online service)
text
xxu
2010
monographic
eng
access
XVIII, 249 p. 36 illus. online resource.
This state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field, including cosmic microwave background analysis, human cortex image denoising, and wireless communication. The work is the first one that combines spline theory (from a numerical or approximation-theoretical view), wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn. Written by internationally renowned mathematicians, the interdisciplinary chapters are expository by design, enabling the reader to understand the theory behind modern image and signal processing methodologies. The main emphasis throughout the book is on the interdependence of the four modern research directions covered. Each chapter ends with exercises that allow for a more in-depth understanding of the material and are intended to stimulate the reader toward further research. A comprehensive index completes the work. Topics covered: * Frames and bases in mathematics and engineering * Wavelets with composite dilations and their applications * Wavelets on the sphere and their applications * Wiener's Lemma: theme and variations Four Short Courses on Harmonic Analysis is intended as a graduate-level textbook for courses or seminars on harmonic analysis and its applications. The work is also an excellent reference or self-study guide for researchers and practitioners with diverse mathematical backgrounds working in different fields such as pure and applied mathematics, image and signal processing engineering, mathematical physics, and communication theory.
Introduction: Mathematical Aspects of Time-Frequency Analysis -- B-Spline Generated Frames -- Continuous and Discrete Reproducing Systems That Arise from Translations. Theory and Applications of Composite Wavelets -- Wavelets on the Sphere -- Wienerâ€™s Lemma: Theme and Variations. An Introduction to Spectral Invariance and Its Applications.
edited by Brigitte Forster, Peter Massopust.
Mathematics
Harmonic analysis
Fourier analysis
Physics
Mathematics
Fourier Analysis
Abstract Harmonic Analysis
Signal, Image and Speech Processing
Theoretical, Mathematical and Computational Physics
QA403.5-404.5
515.2433
Springer eBooks
Applied and Numerical Harmonic Analysis
9780817648916
http://dx.doi.org/10.1007/978-0-8176-4891-6
http://dx.doi.org/10.1007/978-0-8176-4891-6
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