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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.
Electronic books. -- local. --- Frames (Vector analysis). --- Harmonic analysis. --- Wavelets (Mathematics). --- Harmonic analysis --- Civil & Environmental Engineering --- Operations Research --- Engineering & Applied Sciences --- Wavelets (Mathematics) --- Frames (Vector analysis) --- Frame theory (Vector analysis) --- Wavelet analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematics. --- Fourier analysis. --- Physics. --- Fourier Analysis. --- Abstract Harmonic Analysis. --- Signal, Image and Speech Processing. --- Theoretical, Mathematical and Computational Physics. --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Vector analysis --- Analysis, Fourier --- Signal processing. --- Image processing. --- Speech processing systems. --- Mathematical physics. --- Physical mathematics --- Physics --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication)
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