Fast Scalable Image Restoration using Total Variation Priors and Expectation Propagation

TL;DR

This paper introduces a scalable Bayesian approach for image restoration using total variation priors and expectation propagation, enabling efficient MMSE estimation and variance calculation without sampling, suitable for large images.

Contribution

The paper develops a novel EP-based method for TV image restoration that is scalable, parallelizable, and provides accurate posterior estimates without sampling.

Findings

EP achieves comparable accuracy to sampling methods

Method scales efficiently to large images

EP provides reliable variance estimates

Abstract

This paper presents a scalable approximate Bayesian method for image restoration using total variation (TV) priors. In contrast to most optimization methods based on maximum a posteriori estimation, we use the expectation propagation (EP) framework to approximate minimum mean squared error (MMSE) estimators and marginal (pixel-wise) variances, without resorting to Monte Carlo sampling. For the classical anisotropic TV-based prior, we also propose an iterative scheme to automatically adjust the regularization parameter via expectation-maximization (EM). Using Gaussian approximating densities with diagonal covariance matrices, the resulting method allows highly parallelizable steps and can scale to large images for denoising, deconvolution and compressive sensing (CS) problems. The simulation results illustrate that such EP methods can provide a posteriori estimates on par with those obtained via sampling methods but at a fraction of the computational cost. Moreover, EP does not exhibit strong underestimation of posteriori variances, in contrast to variational Bayes alternatives.