2013 Volume 19 Issue 1 Pages 113-119
Fields of experts (FoE) model, which is regarded as a higher-order Markov random field whose clique potentials are modeled by the products of experts, matches spatial structures of natural images well, and therefore, it is an efficient prior of natural images. However, the FoE model does not readily admit efficient inferences because of the complexity of landscape of its energy function. In this paper, we propose an efficient mean field approximation for the FoE model by using a perturbative expansion in statistical mechanics. Our proposed mean field approximation can be applied to the FoE under general settings and can be solved in linear time with respect to the number of pixels. In the latter part of this paper, we apply our method to the image inpainting problem, and we show it gives results being the same or better than ones given by a simple gradient method proposed in the original work.
