High-quality Image Restoration Using Low-Rank Patch Regularization and Global Structure Sparsity

In recent years, approaches based on nonlocal self-similarity and global structure regularization have led to significant improvements in image restoration. Nonlocal self-similarity exploits the repetitiveness of small image patches as a powerful prior in the reconstruction process. Likewise, global structure regularization is based on the principle that the structure of objects in the image is represented by a relatively small portion of pixels. Enforcing this structural information to be sparse can thus reduce the occurrence of reconstruction artifacts. So far, most image restoration approaches have considered one of these two strategies, but not both. This paper presents a novel image restoration method that combines nonlocal self-similarity and global structure sparsity in a single efficient model. Group of similar patches are reconstructed simultaneously, via an adaptive regularization technique based on the weighted nuclear norm. Moreover, global structure is preserved using an innovative strategy, which decomposes the image into a smooth component and a sparse residual, the latter regularized using $l_{1}$ norm. An optimization technique, based on the alternating direction method of multipliers algorithm, is used to recover corrupted images efficiently. The performance of the proposed method is evaluated on two important image restoration tasks: image completion and super-resolution. Experimental results show our method to outperform state-of-the-art approaches for these tasks, for various types and levels of image corruption.