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Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering. A multitude of tools designed to recover hidden information are based on Shannon’s classical sampling theorem, a central pillar of Sampling Theory. The growing need to efficiently obtain precise and tailored digital representations of complex objects and phenomena requires the maturation of available tools in Sampling Theory as well as the development of complementary, novel mathematical theories. Today, research themes such as Compressed Sensing and Frame Theory re-energize the broad area of Sampling Theory. This volume illustrates the renaissance that the area of Sampling Theory is currently experiencing. It touches upon trendsetting areas such as Compressed Sensing, Finite Frames, Parametric Partial Differential Equations, Quantization, Finite Rate of Innovation, System Theory, as well as sampling in Geometry and Algebraic Topology.
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Applied and Numerical Harmonic Analysis Götz E. Pfander Editor Sampling Theory, a Renaissance Compressive Sensing and Other Developments Applied and Numerical Harmonic Analysis Series Editor John J. Benedetto College Park, Maryland, USA Editorial Advisory Board Akram Aldroubi Vanderbilt University TN, USA Gitta Kutyniok Technische Universität Berlin Berlin, Germany Douglas Cochran Arizona State University AZ, USA Mauro Maggioni Duke University NC, USA Hans G. Feichtinger University of Vienna Austria Zuowei Shen National University of Singapore Singapore Christopher Heil Georgia Institute of Technology GA, USA Thomas Strohmer University of California CA, USA Stéphane Jaffard University of Paris XII France Yang Wang Michigan State University MI, USA Jelena Kovaˇcevi´c Carnegie Mellon University PA, USA More information about this series at http://www.springer.com/series/4968 Götz E. Pfander Editor Sampling Theory, a Renaissance Compressive Sensing and Other Developments Editor Götz E. Pfander School of Engineering and Science Jacobs University Bremen Bremen, Germany ISSN 2296-5009 ISSN 2296-5017 (electronic) Applied and Numerical Harmonic Analysis ISBN 978-3-319-19748-7 ISBN 978-3-319-19749-4 (eBook) DOI 10.1007/978-3-319-19749-4 Library of Congress Control Number: 2015953322 Mathematics Subject Classification (2010): 94A20, 94A12, 42C15, 41A45, 30H20 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www. springe