Closed-form Bayesian image denoising: improving the adaptive Wiener filter through pairwise Gaussian-Markov random fields

Abstract

In this paper, we propose a contextual adaptive Wiener filter by using an isotropic pairwise Gaussian Markov random field (GMRF) prior to model the spatial correlation existing in natural images. The motivation for the development of the proposed method is that, in the context of Bayesian estimation, the Wiener filter is known to be the optimal estimator under Gaussian noise. The resulting closed-form filter can be viewed as a two-stage denoising process in which the first stage considers independent pixels whereas the second stage incorporates a degree of spatial dependence by means of maximum pseudo-likelihood estimation of the coupling parameter. The obtained results show that the proposed method outperforms the classical pointwise Wiener filter, in some cases reaching results comparable to some state-of-the-art methods in denoising, but with a reduced computational cost.

Keywords:

• Adaptive Wiener filter; Bayesian estimation; Gaussian–Markov random field; Image denoising; Maximum pseudo-likelihood estimation