Gaussian mixture image restoration based on maximum correntropy criterion

Abstract

Using Gaussian mixture model (GMM) as a patch prior has achieved great success in image restoration (IR). However, based on the derivations, the objective function of the conventional GMM-based IR methods can be expressed as the minimum of mean square error (MMSE) criterion based optimisation problem. As outliers may exist in the patch cluster obtained even within a spatially constrained window and MMSE is sensitive to outliers, using the MMSE criterion based strategy would lead to error results. A maximum correntropy criterion (MCC) based IR method with GMM as a patch prior is proposed. The proposed method can automatically identify outliers and assign weight for each patch within the k-nearest-neighbour patches with respect to each exemplar patch in the image and thus can robustly estimate the Gaussian parameters which results in more accurate estimation of the image patches. Finally, an effective iterative optimisation algorithm is designed to solve the proposed objective function under the MCC criterion. The experimental results for image inpainting demonstrate the capabilities of the proposed method.