Bayesian image restoration under spatially correlated noise-statistical-mechanical approach

In this paper, we discuss the restoration of noise-degraded images through Bayesian inference. Superimposed noise is usually assumed to be uncorrelated between pixels. Here, we discuss spatially correlated noise. The generative statistical models for the original image and the noise are assumed to obey multi-dimensional Gaussian distributions whose covariance matrixes are translational invariant. We can derive an exact description to be used as the expectation for the restored image by means of Fourier transformation. We have attempted to restore a distorted image with spatially correlated noise by using a spatially uncorrelated noise model. We found that the resultant values of the hyperparameter estimations for minimum error and maximal posterior marginal criteria do not coincide with each other when the generative probabilistic model and the model used for the restoration process belong to different classes, while they coincide with each other when these two probabilistic models belong to same class.