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We investigated the use of the Bayesian inference to restore noise-degradedimages under conditions of spatially correlated noise. The generativestatistical models used for the original image and the noise were assumed toobey multi-dimensional Gaussian distributions whose covariance matrices aretranslational invariant. We derived an exact description to be used as theexpectation for the restored image by the Fourier transformation and restoredan image distorted by spatially correlated noise by using a spatiallyuncorrelated noise model. We found that the resulting hyperparameterestimations for the minimum error and maximal posterior marginal criteria didnot coincide when the generative probabilistic model and the model used forrestoration were in different classes, while they did coincide when they werein the same class.Comment: 19 page

Statistical mechanics of the Bayesian image restoration under spatially correlated noise