  This paper presents a new Expectation Propagation (EP) framework for image
restoration using patch-based prior distributions. While Monte Carlo techniques
are classically used to sample from intractable posterior distributions, they
can suffer from scalability issues in high-dimensional inference problems such
as image restoration. To address this issue, EP is used here to approximate the
posterior distributions using products of multivariate Gaussian densities.
Moreover, imposing structural constraints on the covariance matrices of these
densities allows for greater scalability and distributed computation. While the
method is naturally suited to handle additive Gaussian observation noise, it
can also be extended to non-Gaussian noise. Experiments conducted for
denoising, inpainting and deconvolution problems with Gaussian and Poisson
noise illustrate the potential benefits of such flexible approximate Bayesian
method for uncertainty quantification in imaging problems, at a reduced
computational cost compared to sampling techniques.
