Patch-Based Image Restoration using Expectation Propagation

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Abstract

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.
Original languageEnglish
Pages (from-to)192-227
Number of pages36
JournalSIAM Journal on Imaging Sciences
Volume15
Issue number1
Early online date15 Feb 2022
DOIs
Publication statusPublished - Mar 2022

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