Posterior Mean Super-resolution with a Causal Gaussian Markov Random Field Prior

TL;DR

This paper introduces a Bayesian super-resolution method using a causal Gaussian Markov random field prior, employing variational Bayes for stable estimation, and demonstrates improved accuracy over existing techniques.

Contribution

It develops a novel Bayesian super-resolution approach with a causal Gaussian MRF prior and derives the posterior mean estimator using variational Bayes with Taylor approximations.

Findings

The proposed method achieves higher PSNR compared to existing methods.

The approach provides stable and accurate high-resolution images from multiple low-resolution inputs.

Experimental results confirm the effectiveness of the variational Bayes approximation.

Abstract

We propose a Bayesian image super-resolution (SR) method with a causal Gaussian Markov random field (MRF) prior. SR is a technique to estimate a spatially high-resolution image from given multiple low-resolution images. An MRF model with the line process supplies a preferable prior for natural images with edges. We improve the existing image transformation model, the compound MRF model, and its hyperparameter prior model. We also derive the optimal estimator -- not the joint maximum a posteriori (MAP) or marginalized maximum likelihood (ML), but the posterior mean (PM) -- from the objective function of the L2-norm (mean square error) -based peak signal-to-noise ratio (PSNR). Point estimates such as MAP and ML are generally not stable in ill-posed high-dimensional problems because of overfitting, while PM is a stable estimator because all the parameters in the model are evaluated as distributions. The estimator is numerically determined by using variational Bayes. Variational Bayes is a widely used method that approximately determines a complicated posterior distribution, but it is generally hard to use because it needs the conjugate prior. We solve this problem with simple Taylor approximations. Experimental results have shown that the proposed method is more accurate or comparable to existing methods.