Fast Scalable Image Restoration using Total Variation Priors and Expectation Propagation
This work addresses the problem of efficient and accurate image restoration for applications like denoising and deconvolution, offering a scalable solution that is incremental over existing Bayesian methods.
The paper tackles image restoration by developing a scalable approximate Bayesian method using total variation priors and expectation propagation, achieving posterior estimates comparable to sampling methods with significantly lower computational cost.
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.