  We investigated the use of the Bayesian inference to restore noise-degraded
images under conditions of spatially correlated noise. The generative
statistical models used for the original image and the noise were assumed to
obey multi-dimensional Gaussian distributions whose covariance matrices are
translational invariant. We derived an exact description to be used as the
expectation for the restored image by the Fourier transformation and restored
an image distorted by spatially correlated noise by using a spatially
uncorrelated noise model. We found that the resulting hyperparameter
estimations for the minimum error and maximal posterior marginal criteria did
not coincide when the generative probabilistic model and the model used for
restoration were in different classes, while they did coincide when they were
in the same class.
