Bayesian restoration of noisy images with the EM algorithm

In this paper, we demonstrate that a window-based Gaussian mixture model can be applied in the development of a robust nonlinear filter for image restoration. Via the EM algorithm, we utilize ML estimation of the spatially-varying model parameters to achieve the desired noise suppression and detail preservation. We demonstrate that this approach is a powerful tool which gives us information about the local statistics of noisy images. We demonstrate that the estimated local statistics can be efficiently utilized for outlier detection and edge detection. The advantage of our algorithm is that it can simultaneously suppress additive Gaussian and impulsive noise, while preserving fine details and edges.