Image Restoration Using Gaussian Mixture Models With Spatially Constrained Patch Clustering

In this paper, we address the problem of recovering degraded images using multivariate Gaussian mixture model (GMM) as a prior. The GMM framework in our method for image restoration is based on the assumption that the accumulation of similar patches in a neighborhood are derived from a multivariate Gaussian probability distribution with a specific covariance and mean. Previous methods of image restoration with GMM have not considered spatial (geometric) distance between patches in clustering. Our conducted experiments show that in the case of constraining Gaussian estimates into a finite-sized windows, the patch clusters are more likely to be derived from the estimated multivariate Gaussian distributions, i.e., the proposed statistical patch-based model provides a better goodness-of-fit to statistical properties of natural images. A novel approach for computing aggregation weights for image reconstruction from recovered patches is introduced which is based on similarity degree of each patch to the estimated Gaussian clusters. The results admit that in the case of image denoising, our method is highly comparable with the state-of-the-art methods, and our image interpolation method outperforms previous state-of-the-art methods.