Bayesian model selection for unsupervised image deconvolution with structured Gaussian priors

TL;DR

This paper introduces an unsupervised Bayesian framework for image deconvolution, comparing Gaussian models with structured covariances based on their evidence, enabling objective model selection without ground truth.

Contribution

It develops a Bayesian model selection method using marginal likelihood estimation for unsupervised image restoration with structured Gaussian priors.

Findings

Effective model comparison based on evidence without ground truth

Comparison of different Gaussian covariance structures for images and noise

Demonstrated the approach on inverse image restoration problems

Abstract

This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a supervised manner, that can be time-consuming and partly arbitrary. Here we adopt an unsupervised Bayesian approach and objectively compare the models based on their posterior probabilities, directly from the data without ground truth available. The probabilities depend on the marginal likelihood or "evidence" of the models and we resort to the Chib approach including a Gibbs sampler. We focus on the family of Gaussian models with circulant covariances and unknown hyperparameters, and compare different types of covariance matrices for the image and noise.