ENBIS-18 Pre-Conference Course: High-Dimensional Markov Chain Monte Carlo Methods for Bayesian Image Processing Applications

2 September 2018; 14:00 – 18:00; IECL, Faculté des Sciences, Vandoeuvre-lès-Nancy

This half-day course is done under the umbrella of the ENBIS-18 conference in Nancy. You can find more information about the conference here.

 

SUMMARY


Modern signal and image processing methods rely very heavily on probability and statistics to solve challenging problems. Due to the recent increasing interest for high-dimensional data or big data, these problems use more and more complex models, requiring ever more sophisticated computational inference techniques. This course will present an introduction to stochastic simulation methods to sample high-dimensional probability distributions in signal and image processing. A variety of high-dimensional Markov chain Monte Carlo (MCMC) methods will be investigated. The Gibbs sampler will be first considered with some emphasis on its main drawbacks which have led to more elaborated strategies including the block Gibbs sampler, the Metropolis-Hastings Gibbs sampler or the partially collapsed Gibbs sampler. The course will then summarize some methods that have been inspired by results from optimization theory. Some of these methods are based on the discretization of stochastic differential equations resulting from a Langevin diffusion process or from Hamiltonian dynamics. Others use optimization tools such as proximal operators or conjugate gradient iterations. Applications to standard image processing problems such as image denoising, restoration and deconvolution will be used to illustrate the performance of the different Methods. 

 

LECTURERS

Marcelo PEREYRA is an Assistant Professor in Statistics at the School of Mathematics and Computer Sciences of Heriot-Watt University, and the Maxwell Institute for Mathematical Sciences. His research is mainly about new mathematical theory, methods and algorithms to solve inverse problems related to mathematical and computational imaging, with a particular interest in Bayesian analysis and computation. He also serves as Associate Editor for Digital Signal Processing.

Marcelo Pereyra was born in Buenos Aires, Argentina, in 1984. He studied Electronic Engineering and received a double M.Eng. degree from ITBA (Argentina) and INSA Toulouse (France), together with a M.Sc. degree from INSA Toulouse, in June 2009. In July 2012 he obtained a Ph.D. degree in Signal Processing from the University of Toulouse. He is also the recipient of a Marie Curie Intra-European Fellowship for Career Development, a Brunel Postdoctoral Research Fellowship in Statistics, a Postdoctoral Research Fellowship from French Ministry of Defence, a Leopold Escande PhD Thesis excellent award from the University of Toulouse (2012), an INFOTEL R&D excellent award from the Association of Engineers of INSA Toulouse (2009), and an ITBA R&D excellence award from the Buenos Aires Institute of Technology (2007).

 

Jean-Yves TOURNERET (SM’08) received the ingénieur degree in electrical engineering from the Ecole Nationale Supérieure d’Electronique, d’Electrotechnique, d’Informatique, d’Hydraulique et des Télécommunications (ENSEEIHT) de Toulouse in 1989 and the Ph.D. degree from the National Polytechnic Institute from Toulouse in 1992. He is currently a professor in the university of Toulouse (ENSEEIHT) and a member of the IRIT laboratory (UMR 5505 of the CNRS). His research activities are centered around statistical signal and image processing with a particular interest to Bayesian and Markov chain Monte Carlo (MCMC) methods. He has been involved in the organization of several conferences including the European conference on signal processing EUSIPCO'02 (program chair), the international conference ICASSP’06 (plenaries), the statistical signal processing workshop SSP’12 (international liaisons), the International Workshop on Computational Advances in Multi-Sensor Adaptive Processing CAMSAP 2013 (local arrangements), the statistical signal processing workshop SSP'2014 (special sessions), the workshop on machine learning for signal processing MLSP’2014 (special sessions). He has been the general chair of the CIMI workshop on optimization and statistics in image processing hold in Toulouse in 2013 (with F. Malgouyres and D. Kouamé) and of the International Workshop on Computational Advances in Multi-Sensor Adaptive Processing CAMSAP 2015 (with P. Djuric). He has been a member of different technical committees including the Signal Processing Theory and Methods (SPTM) committee of the IEEE Signal Processing Society (2001-2007, 2010-2015). He has been serving as an associate editor for the IEEE Transactions on Signal Processing (2008-2011, 2015-present) and for the EURASIP journal on Signal Processing (2013-present).