Inverse Problems in Imaging and Computer Vision - From Regularization Theory to Bayesian Inference

phies are also mentioned and a common mathematical abstraction for all these inverses problems will be presented. By focusing on a simple linear forward model, first a synthetic analysis of the main deterministic methods (analytical inversion, parametric methods and regularization theory) used in inverse problems is presented and then the focus is given to the Bayesian inference approach. In a first step, the link between Maximum A Posteriori (MAP) and the regularization criteria is described and we will see how different prior modeling result to different regularization criteria. In particular the cases of separable Gaussian and Non-Gaussian, Gauss-Markov and more general Markovian prior models are considered. Then, the advantages of the Bayesian approach to deterministic methods are highlighted through the possibilities of accounting more precisely for uncertainties of the data and model parameters, hyper parameter estimation, marginalization of nuisance parameters and the possibilit...

• Type: Journal
• Year: 2010
• Where: VISAPP
• Authors: Ali Mohammad-Djafari
• Keywords: Computer Vision, Deterministic Methods, Markovian Prior Models, Regularization Criteria, VISAPP 2010