Two-Direction Nonlocal Model for Image Denoising

Similarities inherent in natural images have been widely exploited for image denoising and other applications. In fact, if a cluster of similar image patches is rearranged into a matrix, similarities exist both between columns and rows. Using the similarities, we present a two-directional nonlocal (TDNL) variational model for image denoising. The solution of our model consists of three components: one component is a scaled version of the original observed image and the other two components are obtained by utilizing the similarities. Specifically, by using the similarity between columns, we get a nonlocal-means-like estimation of the patch with consideration to all similar patches, while the weights are not the pairwise similarities but a set of clusterwise coefficients. Moreover, by using the similarity between rows, we also get nonlocal-autoregression-like estimations for the center pixels of the similar patches. The TDNL model leads to an alternative minimization algorithm. Experiments indicate that the model can perform on par with or better than the state-of-the-art denoising methods.