  This paper proposes a general framework for internal patch-based image
restoration based on Conditional Random Fields (CRF). Unlike related models
based on Markov Random Fields (MRF), our approach explicitly formulates the
posterior distribution for the entire image. The potential functions are taken
as proportional to the product of a likelihood and prior for each patch. By
assuming identical parameters for similar patches, our approach can be
classified as a model-based non-local method. For the prior term in the
potential function of the CRF model, multivariate Gaussians and multivariate
scale-mixture of Gaussians are considered, with the latter being a novel prior
for image patches. Our results show that the proposed approach outperforms
methods based on Gaussian mixture models for image denoising and
state-of-the-art methods for image interpolation/inpainting.
