Sparse and Redundant Representations From Theory to Applications in
The field of sparse and redundant representation modeling has gone through a major revolution in the past two decades. This started with a series of algorithms for approximating the sparsest solutions of linear systems of equations, later to be followed b
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Sparse and Redundant Representations From Theory to Applications in Signal and Image Processing
Michael Elad The Technion – Israel Institute of Technology Haifa, Israel
Michael Elad The Technion – Israel Institute of Technology Computer Science Department 32000 Haifa, Israel [email protected]
ISBN 978-1-4419-7010-7 e-ISBN 978-1-4419-7011-4 DOI 10.1007/978-1-4419-7011-4 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010933513 Mathematics Subject Classification (2010): 94A12, 62H35, 62M40, 68U10, 94A08, 94H60, 46N10 © Springer Science+Business Media, LLC 2010 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.springer.com)
To my loving and devoted family, My parents, Rita and Shmuel Elbaz, who have shown me the way, My children Sharon, Adar, and Yuval, who give purpose to this way, and My wife, Ritta, who constantly paves this way with love and understanding.
Foreword
A long long time ago, echoing philosophical and aesthetic principles that existed since antiquity, William of Ockham enounced the principle of parsimony, better known today as Ockham’s razor: “Entities should not be multiplied without necessity.” This principle enabled scientists to select the ”best” physical laws and theories to explain the workings of the Universe and continued to guide scientific research, leading to beautiful results like the minimal description length approach to statistical inference and the related Kolmogorov complexity approach to pattern recognition. However, notions of complexity and description length are subjective concepts and depend on the language “spoken” when presenting ideas and results. The field of sparse representations, that recently underwent a Big-Bang-like expansion, explicitly deals with the Yin-Yang interplay between the parsimony of descriptions and the “language” or “dictionary” used in them, and it became an extremely exciting area of investigation.It already yielded a rich crop of mathematically pleasing, deep and beautiful results that quickly translated into a wealth of practical engineering applications. You are holding in your hands the first guide-book to Sparseland, and I am sure you’ll find in it both familiar and new landscapes to see and admire, as well as excellent pointers that will help you find f
