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This paper considers the objective comparison of stochastic models to solveinverse problems, more specifically image restoration. Most often, modelcomparison is addressed in a supervised manner, that can be time-consuming andpartly arbitrary. Here we adopt an unsupervised Bayesian approach andobjectively compare the models based on their posterior probabilities, directlyfrom the data without ground truth available. The probabilities depend on themarginal likelihood or "evidence" of the models and we resort to the Chibapproach including a Gibbs sampler. We focus on the family of Gaussian modelswith circulant covariances and unknown hyperparameters, and compare differenttypes of covariance matrices for the image and noise.

Bayesian model selection for unsupervised image deconvolution with structured Gaussian priors