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Cover
Title
Copyright
Contents
List of contributors
Preface
1 Introduction to compressed sensing
2 Second-generation sparse modeling: structured and collaborative signal analysis
3 Xampling: compressed sensing of analog signals
4 Sampling at the rate of innovation: theory and applications
5 Introduction to the non-asymptotic analysis of random matrices
6 Adaptive sensing for sparse recovery
7 Fundamental thresholds in compressed sensing: a high-dimensional geometry approach
8 Greedy algorithms for compressed sensing
9 Graphical models concepts in compressed sensing
10 Finding needles in compressed haystacks
11 Data separation by sparse representations
12 Face recognition by sparse representation
Index
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Compressed Sensing Compressed sensing is an exciting, rapidly growing field which has attracted consid- erable attention in electrical engineering, applied mathematics, statistics, and computer science. Since its initial introduction several years ago an avalanche of results have been obtained both of a theoretical as well as practical nature, and various conferences, workshops, and special sessions have been dedicated to this growing research field. This book provides the first detailed introduction to the subject, highlighting recent theoretical advances and a range of applications, as well as outlining numerous remaining research challenges. After a thorough review of the basic theory, many cutting-edge advances in the field are presented, including advanced signal modeling, sub-Nyquist sampling of analog signals, hardware prototypes, non-asymptotic analysis of random matrices, adaptive sensing, greedy algorithms, the use of graphical models, and the separation of morphologically distinct data components. Each chapter is written by leading researchers in the field, and consistent style and notation are utilized throughout. An extended intro- ductory chapter summarizes the basics of the field so that no prior knowledge is required. Key background information and clear definitions make this book an ideal resource for researchers, graduate students, and practitioners wanting to join this exciting research area. It can also serve as a supplementary textbook for courses on computer vision, coding theory, signal processing, image processing, and algorithms for efficient data processing. Yonina C. Eldar is a Professor in the Department of Electrical Engineering at the Tech- nion, Israel Institute of Technology, a Research Affiliate with the Research Laboratory of Electronics at the Massachusetts Institute of Technology, and a Visiting Professor at Stanford University. She has received numerous awards for excellence in research and teaching, including the Wolf Foundation Krill Prize for Excellence in Scientific Research, the Hershel Rich Innovation Award, the Weizmann Prize for Exact Sciences, the Michael Bruno Memorial Award from the Rothschild Foundation, and the Muriel & David Jacknow Award for Excellence in Teaching. She is an Associate Editor for sev- eral journals in the areas of signal processing and mathematics and a Signal Processing Society Distinguished Lecturer. Gitta Kutyniok is an Einstein Professor in the Department of Mathematics at the Tech- nische Universität Berlin, Germany. She has been a Postdoctoral Fellow at Princeton, Stanford, and Yale Universities, and a Full Professor at the Universität Osnabrück, Germany. Her research and teaching have been recognized by various awards, including a Heisenberg Fellowship and the von Kaven Prize by the German Research Founda- tion, an Einstein Chair by the Einstein Foundation Berlin, awards by the Universität Paderborn and the Justus–Liebig Universität Gießen for Excellence in Research, as well as the Weierstraß Prize for Outstanding Teaching. She is an Associate Editor and also Corresponding Editor for several journals in the area of applied mathematics.
Compressed Sensing Theory and Applications Edited by YONINA C. ELDAR Technion-Israel Institute of Technology, Haifa, Israel GITTA KUTYNIOK Technische Universität Berlin, Germany
cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9781107005587 © Cambridge University Press 2012 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2012 Reprinted 2012 Printed and bound in the United Kingdom by the MPG Books Group A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Compressed sensing : theory and applications / edited by Yonina C. Eldar, Gitta Kutyniok. p. cm. Includes bibliographical references and index. ISBN 978-1-107-00558-7 1. Signal processing. QA601.C638 2012 621.382 2011040519 2–dc23 2. Wavelets (Mathematics) I. Eldar, Yonina C. II. Kutyniok, Gitta. ISBN 978-1-107-00558-7 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
Contents List of contributors Preface Introduction to compressed sensing MARK A. DAVENPORT, MARCO F. DUARTE, YONINA C. ELDAR, AND GITTA KUTYNIOK Second-generation sparse modeling: structured and collaborative signal analysis ALEXEY CASTRODAD, PABLO SPRECHMANN, AND GUOSHEN YU IGNACIO RAMIREZ, GUILLERMO SAPIRO, Xampling: compressed sensing of analog signals MOSHE MISHALI AND YONINA C. ELDAR Sampling at the rate of innovation: theory and applications JOSE ANTONIO URIGÜEN, YONINA C. ELDAR, PIER LUIGI DRAGOTTI, AND ZVIKA BEN-HAIM Introduction to the non-asymptotic analysis of random matrices ROMAN VERSHYNIN Adaptive sensing for sparse recovery JARVIS HAUPT AND ROBERT NOWAK Fundamental thresholds in compressed sensing: a high-dimensional geometry approach WEIYU XU AND BABAK HASSIBI Greedy algorithms for compressed sensing THOMAS BLUMENSATH, MICHAEL E. DAVIES, AND GABRIEL RILLING 1 2 3 4 5 6 7 8 page vii ix 1 65 88 148 210 269 305 348
vi 9 10 11 12 Contents Graphical models concepts in compressed sensing ANDREA MONTANARI Finding needles in compressed haystacks ROBERT CALDERBANK AND SINA JAFARPOUR Data separation by sparse representations GITTA KUTYNIOK Face recognition by sparse representation ARVIND GANESH, ANDREW WAGNER, ZIHAN ZHOU, ALLEN Y. YANG, YI MA, AND JOHN WRIGHT Index 394 439 485 515 540
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