Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important mathematical advances
Presents new results and applications to diverse fields such as geometry, number theory, and analysis
Contributors are leading experts in their respective fields
Will be of interest to both pure and applied mathematicians
Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important ma...
This book gives an elementary introduction to a classical area of mathemat- ics - approximation theory - in a way that naturally leads to the modern field of wavelets. The main thread throughout the book is the idea of ap- proximating "complicated expressions" with "simpler expressions," and how this plays a decisive role in many areas of modern mathematics and its applications. One of the main goals of the presentation is to make it clear to the reader that mathematics is a subject in a state of continuous evolution. This fact is usually difficult to explain to students at or near their...
This book gives an elementary introduction to a classical area of mathemat- ics - approximation theory - in a way that naturally leads to the modern f...
The book provides a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image construction and reconstruction. The self-contained survey chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge research and results in the field.
Three main areas are covered: theoretical results, algorithms, and practical applications. Following an historical and introductory overview of the field, the book explores the various mathematical and computational problems of discrete tomography...
The book provides a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image con...
This volume is dedicated to John Benedetto. It seems just yesterday that we celebrated his 60th birthday in a memorable conference in College Park. Yet that was October of 1999, and already more than six years have passed. But John is still too young to be fully honored by a single foreword, or even a singlevolume, thatattemptstosummarizetheimpactofhisworkonharmonic analysis, his students, and his coworkers.Given his continuing high (and even increasing) level of activities, his list of "lifetime achievements" is surely far from complete. Even so, we will make an attempt in this foreword to...
This volume is dedicated to John Benedetto. It seems just yesterday that we celebrated his 60th birthday in a memorable conference in College Park. Ye...
"La narraci6n literaria es la evocaci6n de las nostalgias. " ("Literary narration is the evocation of nostalgia. ") G. G. Marquez, interview in Puerta del Sol, VII, 4, 1996. A Personal Prehistory In 1972 I started cooperating with members of the Biodynamics Research Unit at the Mayo Clinic in Rochester, Minnesota, which was under the direction of Earl H. Wood. At that time, their ambitious (and eventually realized) dream was to build the Dynamic Spatial Reconstructor (DSR), a device capable of collecting data regarding the attenuation of X-rays through the human body fast enough for...
"La narraci6n literaria es la evocaci6n de las nostalgias. " ("Literary narration is the evocation of nostalgia. ") G. G. Marquez, interview in Puerta...
Overview For over a decade now, wavelets have been and continue to be an evolving subject of intense interest. Their allure in signal processing is due to many factors, not the least of which is that they offer an intuitively satisfying view of signals as being composed of little pieces of wa'ues. Making this concept mathematically precise has resulted in a deep and sophisticated wavelet theory that has seemingly limitless applications. This book and its supplementary hands-on electronic: component are meant to appeal to both students and professionals. Mathematics and en- gineering students...
Overview For over a decade now, wavelets have been and continue to be an evolving subject of intense interest. Their allure in signal processing is du...
The aim of this work is to present several topics in time-frequency analysis as subjects in abelian group theory. The algebraic point of view pre- dominates as questions of convergence are not considered. Our approach emphasizes the unifying role played by group structures on the development of theory and algorithms. This book consists of two main parts. The first treats Weyl-Heisenberg representations over finite abelian groups and the second deals with mul- tirate filter structures over free abelian groups of finite rank. In both, the methods are dimensionless and coordinate-free and apply...
The aim of this work is to present several topics in time-frequency analysis as subjects in abelian group theory. The algebraic point of view pre- dom...
In 1994, in my role as Technical Program Chair for the 17th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, I solicited proposals for mini-symposia to provide delegates with accessible summaries of important issues in research areas outside their particular specializations. Terry Peters and his colleagues submitted a proposal for a symposium on Fourier Trans- forms and Biomedical Engineering whose goal was "to demystify the Fourier transform and describe its practical application in biomedi- cal situations." This was to be achieved by presenting the...
In 1994, in my role as Technical Program Chair for the 17th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, I...
In his paper Theory of Communication Gab46], D. Gabor proposed the use of a family of functions obtained from one Gaussian by time-and frequency- shifts. Each of these is well concentrated in time and frequency; together they are meant to constitute a complete collection of building blocks into which more complicated time-depending functions can be decomposed. The application to communication proposed by Gabor was to send the coeffi- cients of the decomposition into this family of a signal, rather than the signal itself. This remained a proposal-as far as I know there were no seri- ous...
In his paper Theory of Communication Gab46], D. Gabor proposed the use of a family of functions obtained from one Gaussian by time-and frequency- shi...
"D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material . . . than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform . . . The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended "
--Bulletin of the AMS
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"D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material . . . than is typically...
