Shearlets : Multiscale Analysis For Multivariate Data

Applied and Numerical Harmonic Analysis Series Editor John J. Benedetto University of Maryland College Park, MD, USA Editorial Advisory Board Akram Aldroubi Vanderbilt University Nashville, TN, USA Jelena Kovaˇcevi´c Carnegie Mellon University Pittsburgh, PA, USA Andrea Bertozzi University of California Los Angeles, CA, USA Gitta Kutyniok Technische Universit¨at Berlin Berlin, Germany Douglas Cochran Arizona State University Phoenix, AZ, USA Mauro Maggioni Duke University Durham, NC, USA Hans G. Feichtinger University of Vienna Vienna, Austria Zuowei Shen National University of Singapore Singapore, Singapore Christopher Heil Georgia Institute of Technology Atlanta, GA, USA Thomas Strohmer University of California Davis, CA, USA St´ephane Jaffard University of Paris XII Paris, France Yang Wang Michigan State University East Lansing, MI, USA For further volumes: http://www.springer.com/series/4968 Gitta Kutyniok • Demetrio Labate Editors Shearlets Multiscale Analysis for Multivariate Data Editors Gitta Kutyniok Institut f¨ur Mathematik Technische Universit¨at Berlin Berlin, Germany Demetrio Labate Department of Mathematics University of Houston Houston, TX, USA ISBN 978-0-8176-8315-3 e-ISBN 978-0-8176-8316-0 DOI 10.1007/978-0-8176-8316-0 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2012932597 Mathematical Subject Classification (2010): 42C15, 42C40, 65T60, 68U10, 94A08 c Springer Science+Business Media, LLC 2012  All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.birkhauser-science.com) ANHA Series Preface The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract harmonic analysis to basic applications. The title of the series reflects the importance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbiotic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has flourished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship between harmonic analysis and fields such as signal processing, partial differential equations (PDEs), and image processing is reflected in our state-of-theart ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time–frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them. For example, wavelet theory can be considered an appropriate tool to deal with some basic problems in digital signal processing, speech and image p