Low rank regularization exploiting intra and inter patch correlation for image denoising
Based on the observation that a matrix X consisted of non-local highly-correlated patches is of low rank, many image restoration methods use low-rank regularization to exploit correlation between image contents, so that the uncertainty of the unknown image signal can be reduced. To tackle the problem that the underlying cost function to pursue minimal rank is hard to solve, an effective way is to employ smooth non-convex surrogate log |XXT| for the rank penalty. Essentially, such technique only considers to utilize correlation within image patches. 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 signal, and thus improve the prediction of the latent image. The corresponding two surrogates are integrated to incorporate both intra- and inter-patch correlation. To solve 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 show that the proposed approach outperforms several state-of-the-art methods in terms of PSNR and perceptual quality.