Continuous MRF based image denoising with a closed form solution

In this paper, we formulate the problem of image denoising as the maximum a posterior (MAP) estimation problem using Markov random fields (MRFs). Such an MAP estimation for MRFs is equivalent to a maximum likelihood estimation constrained on spatial homogeneity and is generally NP-hard in the discrete domain. To make it tractable, we convert it to a continuous label assignment problem based on a Gaussian MRF model and then obtain a closed form globally optimal solution. Since the Gaussian MRFs tend to over-smooth images and blur edges, we incorporate pre-estimated image edge information into the energy function to better preserve image structures. Patch similarity based pairwise interaction is also involved to better preserve image details and make the algorithm more robust to impulse noise. Both quantitative and qualitative comparative experimental results are given to demonstrate the better performance of our algorithm.