Hyperparameter Estimation in Bayesian Image Superresolution with a Compound Markov Random Field Prior

We address the hyperparameter estimation problem in Bayesian image superresolution with a compound Gaussian Markov random field (MRF) prior. Superresolution aims at reconstructing a high-resolution (HR) image from low-resolution degraded observations, and the compound MRF enables edge-preserving superresolution owing to the additional layer of edge representation. In addition to the regularization hyperparameters, the compound model has an additional hyperparameter of the edge bias that controls the probability of edge presence. We estimate all the hyperparameters, the registration parameters, and the HR image by means of minimizing variational free energy under the assumption of a factorized posterior. Experiments show that automatic determination of the hyperparameters including the bias and the regularization parameters, as well as edge- preserving superresolution of the HR image, is successfully accomplished by the proposed method.