Bayesian and regularization methods for hyperparameter estimation in imagerestoration

In this paper, we propose the application of the hierarchical Bayesian para digm to the image restoration problem. We derive expressions for the iterat ive evaluation of the two hyperparameters applying the evidence and maximum a posteriori (MAP) analysis within the hierarchical Bayesian paradigm. We show analytically that the analysis provided by the evidence approach is mo re realistic and appropriate than the MAP approach for the image restoratio n problem, We furthermore study the relationship between the evidence and a n iterative approach resulting from the set theoretic regularization approa ch for estimating the two hyperparameters, or their ratio, defined as the r egularization parameter, Finally the proposed algorithms are tested experim entally.