A Non-local Method for Robust Noisy Image Completion

The problem of noisy image completion refers to recovering an image from a random subset of its noisy intensities. In this paper, we propose a non-local patch-based algorithm to settle the noisy image completion problem following the methodology “grouping and collaboratively filtering”. The target of “grouping” is to form patch matrices by matching and stacking similar image patches. And the “collaboratively filtering” is achieved by transforming the tasks of simultaneously estimating missing values and removing noises for the stacked patch matrices into low-rank matrix completion problems, which can be efficiently solved by minimizing the nuclear norm of the matrix with linear constraints. The final output is produced by synthesizing all the restored patches. To improve the robustness of our algorithm, we employ an efficient and accurate patch matching method with adaptations including pre-completion and outliers removal, etc. Experiments demonstrate that our approach achieves state-of-the-art performance for the noisy image completion problem in terms of both PSNR and subjective visual quality.