An implicit Markov random field model for the multi-scale oriented representations of natural images

In this paper, we describe a new Markov random field (MRF) model for natural images in multiscale oriented representations. The MRF in this model is specified with the singleton conditional densities (the density of one subband coefficient given its Markovian neighbors), while the clique potentials and joint density of this model are implicitly defined. The singleton conditional densities are chosen to have maximum entropy and consistent with observed statistical properties of natural images. We then describe parameter learning for this model, and a sparse prior to choose optimal model structure. Using this model as image prior, we develop an iterative image denoising method, and a solution to restoring images with missing blocks of subband coefficients.