Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity

This book presents the state of the art in sparse and multiscale image and signal processing, covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Recent concepts of sparsity and morphological diversity are described and exploited for various problems such as denoising, inverse problem regularization, sparse signal decomposition, blind source separation, and compressed sensing. This book weds theory and practice in examining applications in areas such as astronomy, biology, physics, digital media, and forensics. A final chapter explores a paradigm shift in signal processing, showing that previous limits to information sampling and extraction can be overcome in very significant ways. Matlab and IDL code accompany these methods and applications to reproduce the experiments and illustrate the reasoning and methodology of the research available for download at the associated Web site.

This book presents the state of the art in sparse and multiscale image and signal processing, covering linear multiscale transforms, such as wavelet, ridgelet, or curvelettransforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Recent concepts of sparsity and morphological diversity are described and exploited for various problems such as denoising, inverse problem regularization, sparse signal decomposition, blind source separation, and compressed sensing.

This book weds theory and practice in examining applications in areas such as astronomy, biology, physics, digital media, and forensics. A final chapter explores a paradigm shift in signal processing, showing that previous limits to information sampling and extraction can be overcome in very significant ways.

MATLAB and IDL code accompany these methods and applications to reproduce the experiments and illustrate the reasoning and methodology of the research available for download at the associated Web site.

Jean-Luc Starck is a researcher at the Institute of Research into the Fundamental Laws of the Universe (IRFU), CEA-Saclay. He holds a Ph.D. from the University of Nice-Sophia Antipolis and Observatory of Côte d'Azur and a habilitation degree from the University Paris XI. He is a former visiting researcher at the European Southern Observatory (ESO), UCLA, and the Statistics Department at Stanford University. His research interests include image processing, statistical methods in astrophysics, and cosmology. He is also author of two books, entitled Image Processing and Data Analysis: The Multiscale Approach and Astronomical Image and Data Analysis.

Fionn Murtagh directs Ireland's Science Foundation funding programs in Information and Communications Technologies and Energy. He holds a Ph.D. from the Université Paris 6 and a habilitation from Université de Strasbourg. Murtagh held professorial chairs at the University of Ulster, Queen's University Belfast, and now at Royal Holloway, University of London. He is a Fellow of the International Association for Pattern Recognition, a Fellow of the British Computer Society, and an elected Member of the Royal Irish Academy.

Jalal M. Fadili graduated from the Ecole Nationale Supérieure d'Ingénieurs (ENSI) de Caen, France, and received MSc and Ph.D. degrees in signal and image processing from the University of Caen. He was a Research Associate with the University of Cambridge (McDonnell–Pew Fellow) from 1999 to 2000. He has been an Associate Professor of signal and image processing since September 2001 at ENSI. He was a visitor at several universities (QUT-Australia, Stanford University, CalTech, EPFL). His research interests include mathematical signal and image processing, statistics, optimization theory, and sparse representations.