Four Short Courses on Harmonic Analysis: Wavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis (Applied and Numerical Harmonic Analysis)

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9780817648909: Four Short Courses on Harmonic Analysis: Wavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis (Applied and Numerical Harmonic Analysis)
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Written by internationally renowned mathematicians, this state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field. The work is the first one that combines spline theory, wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn.

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.

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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.

Review:

From the reviews:

“This is a well-written, advanced textbook on harmonic analysis intended for graduate students, mathematicians, and engineers working in signal processing and communications technology. The book is based on a number of lectures given at the summer school on New Trends and Directions in Harmonic Analysis, Approximation Theory, and Image Analysis...
     The book is divided into five chapters, and each chapter concludes with a number of exercises of varying complexity. The first chapter contains a general introduction to the topic and to the terms used in the subsequent four chapters.
     The specific topics covered in Chapters 2–5 are:  frames and bases in mathematics and engineering, wavelets with composite dilation and their applications, wavelets on the sphere and their applications, and finally Wiener's Lemma: theme and variations.”   ―Mathematical Reviews

“The authors introduce the reader to their recent work in new areas of harmonic analysis. ... The treatment of each topic is primarily mathematical, mostly targeting pure mathematicians and mathematical physicists in the fields of image and signal processing. ... As an engineer, I found the book helpful in providing mathematical basis/direction for new techniques in time-frequency analysis of signals.” (Menachem Rafaelof, Noise Control Engineering Journal, Vol. 58 (5), September-October, 2010)

“The present texts consists of four lectures on recent topics in time-frequency analysis which grew out of a summer school, together with an introductory chapter with background material by the editors. ... All chapters are well written and provide a good introduction to their respective subjects. ... In summary, it is a good starting point for students with a basic background in harmonic analysis as well as for researchers working in this area.” (G. Teschl, Monatshefte für Mathematik, Vol. 162 (4), April, 2011)

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