Steele Prize for excellence in expository writing. Ingrid Daubechies received the National Academy of Sciences NAS Award in Mathematics, which is given every four years for excellence in published mathematical research. Daubechies was chosen "for fundamental discoveries on wavelets and wavelet expansions and for her role in making wavelet methods a pracical basic tool of applied mathematics". Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. They are a fairly simple mathematical tool now being applied to the compression of data--such as fingerprints, weather satellite photographs, and medical x-rays--that were previously thought to be impossible to condense without losing crucial details.
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They are a fairly simple mathematical tool now being applied to the compression of data—such as fingerprints, weather satellite photographs, and medical x-rays—that were previously thought to be impossible to condense without losing crucial details. This monograph contains 10 lectures presented by Dr. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient.
The opening chapter provides an overview of the main problems presented in the book. Following chapters discuss the theoretical and practical aspects of wavelet theory, including wavelet transforms, orthonormal bases of wavelets, and characterization of functional spaces by means of wavelets.
The last chapter presents several topics under active research, as multidimensional wavelets, wavelet packet bases, and a construction of wavelets tailored to decompose functions defined in a finite interval. Because of their interdisciplinary origins, wavelets appeal to scientists and engineers of many different backgrounds. Their name itself was coined approximately a decade ago Morlet, Arens, Fourgeau, and Giard , Morlet , Grossmann and Morlet ; in the last ten years interest in them has grown at an explosive rate.
There are several reasons for their present success. As a consequence of these interdisciplinary origins, wavelets appeal to scientists and engineers of many different backgrounds. On the other hand, wavelets are a fairly simple mathematical tool with a great variety of possible applications. Already they have led to exciting applications in signal analysis sound, images some early references are Kronland-Martinet, Morlet and Grossmann , Mallat b , c ; more recent references are given later and numerical analysis fast algorithms for integral transforms in Beylkin, Coifman, and Rokhlin ; many other applications are being studied.
This wide applicability also contributes to the interest they generate. Battle, G. Beylkin, C. Chui, A. Cohen, R. Coifman, K.
Liandrat, S. Mallat, B. Willsky provided lectures on their work related to wavelets. Moreover, three workshops were organized, on applications to physics and inverse problems chaired by B. DeFacio , group theory and harmonic analysis H.
Feichtinger , and signal analysis M. The audience consisted of researchers active in the field of wavelets as well as of mathematicians and other scientists and engineers who knew little about wavelets and hoped to learn more. This second group constituted the largest part of the audience.
I saw it as my task to provide a tutorial on wavelets to this part of the audience, which would then be a solid grounding for more recent work exposed by the other lecturers and myself.
She received her B. In she constructed a class of wavelets that were identically zero outside a finite interval, now among the most common type of wavelets used in applications. She was the first woman full professor of mathematics at Princeton. In she was elected as the first woman president of the International Mathematical Union. She is currently the James B. Duke Professor of Mathematics at Duke University. Daubechies received the Louis Empain Prize for Physics in , awarded once every five years to a Belgian scientist on the basis of work done before age
Ten lectures on wavelets
Thus, as a child, she already familiarized herself with the properties of exponential growth. Her parents found out that mathematical conceptions, like cone and tetrahedron , were familiar to her before she reached the age of 6. She excelled at the primary school, moved up a class after only 3 months. During the next few years, she visited the CNRS Center for Theoretical Physics in Marseille several times, where she collaborated with Alex Grossmann ; this work was the basis for her doctorate in quantum mechanics.