Image Denoising via Low Rank Regularization Exploiting Intra and Inter Patch Correlation

In image restoration tasks, image priors generally utilize correlation within image contents to predict the latent image signal. In this paper, we propose to jointly exploit both intra- and inter-patch correlation of the input image, so as to further reduce the uncertainty of the unknown signal, and thus improve the prediction of the latent image. The proposed scheme evolves from the low-rank regularization for non-local highly-correlated image contents. Since the underlying cost function to pursue minimal rank is hard to solve, we use non-convex smooth surrogates for the rank penalty. Two such surrogates are utilized in order to incorporate both intra- and inter-patch correlation. To tackle the optimization problem, we use iterative alternating direction technique to divide the problem into two subproblems, each of which is solved via an empirical Bayesian procedure built upon variational approximation. Experimental results on image denoising show that the proposed approach outperforms several state-of-the-art methods in terms of peak signal-to-noise ratio, structural similarity, and perceptual quality.