ENBIS-18 in Nancy

2 – 25 September 2018; Ecoles des Mines, Nancy (France) Abstract submission: 20 December 2017 – 4 June 2018

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

2 September 2018, 14:00 – 18:00

This half-day ENBIS-18 pre-conference workshop will be given by Marcelo PEREYRA and Jean-Yves TOURNERET and can be booked here.

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. 

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