Fundamental Papers in Wavelet Theory by Christopher Heil (PDF)

Description

This book traces the prehistory and initial development of wavelet theory, a discipline that has had a profound impact on mathematics, physics, and engineering. Interchanges between these fields during the last fifteen years have led to a number of advances in applications such as image compression, turbulence, machine vision, radar, and earthquake prediction. This book contains the seminal papers that presented the ideas from which wavelet theory evolved, as well as those major papers that developed the theory into its current form. These papers originated in a variety of journals from different disciplines, making it difficult for the researcher to obtain a complete view of wavelet theory and its origins. Additionally, some of the most significant papers have heretofore been available only in French or German. Heil and Walnut bring together these documents in a book that allows researchers a complete view of wavelet theory’s origins and development.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a lovely collection of papers coming out of the last two or three decades of mathematical trends connected in one way or the other to wavelets.A current 2006 google search on “wavelet” yields 6,470,000 hits; many of them dealing with applications, for example signal and image processing. The volume brings to light even more interdisciplinary trends. I expect the book will be a valued source for students in math, in applications, and in engineering. The book is divided into seven parts, and each part is given an attractive and well written introduction, written by an expert in the field. Several of the selected papers have served as precursors for major advances in one or the other of the central areas of the subject. The Foreword is written especially for students and it is by Ingrid Daubechies. The individual authors who wrote the seven current and separate introductions to the seven parts of the book are Jelena Kovacevic (signal processing), Jean-Pierre Antoine (physics, coherent states), Hans Feichtinger (precursors of wavelet bases), Yves Meyer (harmonic analysis and atomic decompositions), Guido Weiss (multiresolutions, multivariable theory), and Mladen V. Wickerhauser (applications, computations, image coding and more.) And there is a charming introduction to the entire collection written by John Benedetto. It is delightful and full of insight. The historical comments are fascination too. The editor Chris Heil did a wonderful job: The present selection of original papers in the area is meant to offer motivation, and history; and more importantly it serves as a guide to students trying to learn some of this. The chosen papers are on target, and each section is nicely introduced so that it will help students getting into anyone of the many aspects of wavelet mathematics. Some of the original and older papers (Haar, Meyer, …) were in French or German, and they have now been translated. Excellent translations! The total number of pages is a little less than 900, but even so, there is a lot more to say, for example about connections to computer graphics.Review by Palle Jorgensen, October 2006.

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