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This book introduces 2-D wavelets via 1-D continuous wavelet transforms. The authors then describe the underlying mathematics before progressing to more advanced topics such as matrix geometry of wavelet analysis and three-dimensional wavelets. Practical applications and illustrative examples are employed extensively throughout, ensuring the book's value to engineers, physicists and mathematicians. Two-dimensional wavelets offer a number of advantages over discrete wavelet transforms, in particular, for analysis of real-time signals in such areas as medical imaging, fluid dynamics, shape recognition, image enhancement and target tracking.
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Two-Dimensional Wavelets and their Relatives
Two-dimensional wavelets offer a number of advantages over discrete wavelet transforms when processing rapidly varying functions and signals. In particular, they offer benefits for real-time applications such as medical imaging, fluid dynamics, shape recognition, image enhancement and target tracking. This book introduces the reader to 2-D wavelets via 1-D continuous wavelet transforms, and includes a long list of useful applications. The authors then describe in detail the underlying mathematics before moving on to more advanced topics such as matrix geometry of wavelet analysis, three-dimensional wavelets and wavelets on a sphere. Throughout the book, practical applications and illustrative examples are used extensively, ensuring the book’s value to engineers, physicists and mathematicians alike. Jean-Pierre Antoine is a Professor of Mathematical Physics at the Institut de Physique
Th´eorique, Universit´e Catholique de Louvain. Romain Murenzi is currently Minister of Education, Science, Technology, and Scientific
Research of the Republic of Rwanda, on leave of absence from the Department of Physics, Clark Atlanta University, Atlanta, Georgia. Pierre Vandergheynst is a Professor at the Signal Processing Institute, Swiss Federal
Institute of Technology, Lausanne. Syed Twareque Ali is a Professor at the Department of Mathematics and Statistics, Concordia University, Montr´eal.
Two-Dimensional Wavelets and their Relatives Jean-Pierre Antoine Institut de Physique Th´eorique, Universit´e Catholique de Louvain
Romain Murenzi CTSPS, Clark Atlanta University, Ministry of Education, Science, Technology and Scientific Research, Rwanda
Pierre Vandergheynst Signal Processing Laboratory, Swiss Federal Institute of Technology
Syed Twareque Ali Department of Mathematics and Statistics, Concordia University
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge , UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521624060 © J.-P. Antoine, R. Murenzi, P. Vandergheynst and S. Twareque Ali 2004 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2004 - -
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Contents
Prologue
page ix
1
Warm-up: the 1-D continuous wavelet transform