Deterministic and Bayesian Sparsity enforcing models in signal and image processing
In this talk, first examples of sparse signals and images are presented. Then, different deterministic ways of modeling and sparse representation methods and algorithms (MP, OMP, LASSO, IHT, ADMM …) are summarized. The Bayesian Maximum A Posteriori (MAP) approach and its link with regularization is mentioned. The prior models which enforce sparsity are classified in four main classes:
- Heavy tailed: Double Exponential, Generalized Gaussian, Student-t, Cauchy;
- Mixture models: Finite mixture of Gaussians,
- Infinite Scaled Gaussian mixture model and its relation to Student-t and their equivalent hierarchical models with hidden variables;
- General Gauss-Markov-Potts models.
Using these priors in a Bayesian approach needs appropriate computational tools which are summarized as: Joint Maximum A Posteriori (JMAP), MCMC and Variational Bayesian Approximation (VBA). Finally, the applications of these prior models in Inverse Problems such as X ray Computed Tomography and Microwave inverse scattering imaging systems are presented.
Ali Mohammad-Djafari received the B.Sc. degree in electrical engineering from Polytechnic of Teheran, in 1975, the diploma degree (M.Sc.) from Ecole Supérieure d’Electricité (SUPELEC), Gif sur Yvette, France, in 1977, the “Docteur-Ingénieur” (Ph.D.) degree and “Doctorat d’Etat” in Physics, from the University of Paris Sud 11 (UPS), Orsay, France, respectively in 1981 and 1987.
He was Assistant Professor at UPS for two years (1981-1983). Since 1984, he has a permanent position at “Centre national de la recherche scientifique (CNRS)” and works at “Laboratoire des signaux et systèmes (L2S)” at Centrale-Supélec. He was a visiting Associate Professor at University of Notre Dame, Indiana, USA during 1997-1998. From 1998 to 2002, he has been at the head of Signal and Image Processing division at this laboratory. Presently, he is “Directeur de recherche” and his main scientific interests are in developing new probabilistic methods based on Bayesian inference, Information Theory and Maximum Entropy approaches for Inverse Problems in general in all aspects of data processing, and more specifically in imaging and vision systems: image reconstruction, signal and image deconvolution, blind source separation, sources localization, data fusion, multi and hyper spectral image segmentation. The main application domains of his interests are Medical imaging, Computed Tomography (X rays, PET, SPECT, MRI, microwave, ultrasound and eddy current imaging) either for medical imaging or for Non Destructive Testing (NDT) in industry, multivariate and multi-dimensional data, space-time signal and image processing, data mining, clustering, classification and machine learning methods for biological or medical applications. He has supervised more than 20 Ph.D. Thesis, more than 20 Post-doc research activities and more than 50 M.Sc. Student research projects. He has more than 60 full journal papers and more than 300 papers in national and international conferences. He has organized or co-organized more than 10 international workshops and conferences. He has been expert for a great number of French national and international projects. Since 1988 he has many teaching activities in M.Sc. and Ph.D. Level in SUPELEC, University of Paris sud, ENSTA and Ecole centrale de Paris.