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The color video inpainting problem is one of the most challenging problem inthe modern imaging science. It aims to recover a color video from a small partof pixels that may contain noise. However, there are less of robust models thatcan simultaneously preserve the coupling of color channels and the evolution ofcolor video frames. In this paper, we present a new robust quaternion tensorcompletion (RQTC) model to solve this challenging problem and derive the exactrecovery theory. The main idea is to build a quaternion tensor optimizationmodel to recover a low-rank quaternion tensor that represents the targetedcolor video and a sparse quaternion tensor that represents noise. This newmodel is very efficient to recover high dimensional data that satisfies theprior low-rank assumption. To solve the case without low-rank property, weintroduce a new low-rank learning RQTC model, which rearranges similar patchesclassified by a quaternion learning method into smaller tensors satisfying theprior low-rank assumption. We also propose fast algorithms with globalconvergence guarantees. In numerical experiments, the proposed methodssuccessfully recover color videos with eliminating color contamination andkeeping the continuity of video scenery, and their solutions are of higherquality in terms of PSNR and SSIM values than the state-of-the-art algorithms.

A New Low-Rank Learning Robust Quaternion Tensor Completion Method for Color Video Inpainting Problem and Fast Algorithms