Sparse image and signal processing wavelets, curvelts, morphological diversitySPARSE MAGE ANDSIGNA PRoCESSiNGWavelets, Curvelets,Morphological DiversityJean-Luc starckCentre d' Etudes de saclay, franceFionn MurtaghRoyal Holloway, University of LondonJa|a|M。 FadiliEcole Nationale Superieure d'Ingenieurs, Cael即罗CAMBRIDGEUNIVERSITY PRESSCAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town, SingaporeSao Paulo, Delhi, Dubai, TokyoCambridge University Press32 Avenue of the americas New York. NY 10013-2473 USAwww.cambridge.orgInformationonthistitlewww.cambridge.org/9780521119139C Jean-Luc Starck, Fionn Murtagh, and Jalal M. Fadili 2010This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreementsno reproduction of any part may take place without the writtenpermission of Cambridge University PressFirst published 2010Printed in the United States of Americaa catalog record for this publication is available from the british LibraryLibrary of Congress Cataloging in Publication dataStarck, J.-L. Jean-Luc), 1965Sparse image and signal processing: wavelets, curvelets, morphologicaldiversity /Jean-Luc Starck, Fionn Murtagh, Jalal FadiliIncludes bibliographical references and indexISBN9780-521-11913-9( hardback)1. Transformations(Mathematics) 2. Signal processing. 3. Image processing4. Sparse matrices. 5. Wavelets(Mathematics) I Murtagh, Fionn. II. Fadili,Jalal. 1973- IIl. TitleQA601S7852010621.367-dc222009047391isbn 978-0-521-11913-9 HardbackAdditionalresourcesforthispublicationatwww.Sparsesignalrecipes.infoCambridge University Press has no responsibility for the persistence oraccuracy of URLS for external or third-party Internet Web sites referred to inthis publication and does not guarantee that any content on such Web sites is,or will remain, accurate or appropriateContentsAcronymspage IxNotationPrefaceXⅤ1 Introduction to the World of Sparsity1.1 Sparse representation1.2 From fourier to wavelets11561.3 From Wavelets to Overcomplete Representations1. 4 Novel Applications of the wavelet and curvelet transforms81.5 Summary152 The wavelet transform,162.1 Introduction162. 2 The Continuous wavelet transform162.3 Examples of Wavelet Functions182.4 Continuous wavelet Transform algorithm212. 5 The discrete wavelet transform222.6 Nondyadic Resolution factor282. 7 The lifting Scheme312. 8 Wavelet Packets342.9 Guided Numerical Experiments382.10 Summary443 Redundant wavelet transform453.1 Introduction453.2 The Undecimated wavelet Transform463.3 Partially decimated wavelet transform493.4 The Dual-Tree complex wavelet transform513.5 Isotropic Undecimated wavelet Transform: Starlet Transform533.6 Nonorthogonal Filter Bank design583.7 Pyramidal wavelet Transformontents3.8 Guided Numerical Experiments693.9 Summary744 Nonlinear multiscale transforms,,754.1 Introduction754.2 Decimated nonlinear transform754.3 Multiscale Transform and Mathematical Morphology774.4 Multiresolution based on the median transform814.5 Guided Numerical Experiments864.6 Summary885 The Ridgelet and Curvelet Transforms■■■■■■89895.2 Background and Example893 Ridgelets915.4 Curvelets1005.5 Curvelets and Contrast Enhancement5.6 Guided Numerical Experiments1125.7 Summary6 Sparsity and Noise Removal.1196.1 Introductio1196.2 Term-By-Term Nonlinear Denoisin1206.3 Block Nonlinear Denoising1276.4 Beyond Additive Gaussian Noise1326. 5 Poisson noise and the haar transform1346.6 Poisson noise with low counts1366.7 Guided Numerical experiments1436. 8 Summary1457 Linear Inverse Problems1497.1 Introduction1497.3 Monotone Operator Splitting Framework ms7.2 Sparsity-Regularized Linear Inverse Proble1511527.4 Selected Problems and algorithms1607.5 Sparsity Penalty with Analysis Prior1707.6 Other Sparsity-Regularized Inverse Problems1727.7 General Discussion: Sparsity, Inverse Problems, and IterativeThresholding1747.8 Guided Numerical Experiments1767.9 Summary1788 Morphological Diversity1808.1 ntroduction1808.2 Dictionary and Fast Transformation1838.3 Combined denoising1838.4 Combined deconvolution1888.5 Morphological Component Analysis190Contents8.6 Texture-Cartoon Separation1988.7 Inpainting2048.8 Guided Numerical Experiments2108.9 Summary2169 Sparse Blind Source Separation,,,2189. 1 Introduction2189.2 Independent Component analysis2209.3 Sparsity and Multichannel Data2249. 4 Morphological Diversity and Blind Source Separation2269.5 Illustrative Experiments2379.6 Guided Numerical Experiments2429.7 Summary24410 Multiscale Geometric Analysis on the Sphere24510.1 Introduction24510.2 Data on the sphere24610.3 Orthogonal Haar Wavelets on the Sphere24810.4 Continuous wavelets on the sphere24910.5 Redundant wavelet Transform on the Sphere with ExactReconstruction25310.6 Curvelet Transform on the Sphere26110.7 Restoration and Decomposition on the sphere26610.8 Applications26910.9 Guided Numerical Experiments27210.10 Summary27611 Compressed Sensing。,,,27711.1 Introduction27711.2 Incoherence and Sparsity27811. 3 The sensing protocol27811.4 Stable Compressed Sensing8011.5 Designing Good Matrices: Random Sensing28211.6 Sensing with Redundant Dictionaries11.7 Compressed Sensing in Space Science28311.8 Guided Numerical Experiments28511.9 Summary286References289List of algorithms311Index313Color Plates follow page 148Acronyms1-D.2-D.3-Done-dimensional two-dimensional three-dimensionalAACadvanced audio codingAICakaike information criterionBCRblock-coordinate relaxationBICBayesian information criterionBPbasis pursuitBPDNbasis pursuit denoisingBSSblind source separationCCDcharge-coupled deviceCeCILLCEA CNRS INRIA Logiciel LibreCMBcosmic microwave backgroundCOBECosmic background ExplorerCTScurvelet transform on the sphereCScompressed sensingCWTcontinuous wavelet transformdBdecibelDCTdiscrete cosine transformDCTGl, DCTG2 first-generation discrete curvelet transform secondgeneration discrete curvelet transformDRDouglas-RachfordDRTdiscrete ridgelet transformDWTdiscrete wavelet transformECPequidistant coordinate partitionEEGelectroencephalographyEFICAefficient fast independent component analysisEMexpectation maximizationERSEuropean remote sensingESAEuropean Space agencyFBforward-backwardFDRfalse discovery rateFFTfast fourier transform