Prof. Ali Mohammad-Djafari——遥感科学国家重点实验室2016年系列学术讲座之五十六
报告题目：Sparsity enforcing models in signal and image processing: A survey of deterministic and Bayesian approaches and computational algorithms
报告人：Prof. Ali Mohammad-Djafari（Research Director in CNRS, France）
报告人简介：Ali Mohammad-Djafari is "Directeur de recherche" in Centre national de la recherche scientifique (CNRS) 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.
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.