A New Low-Rank Learning Robust Quaternion Tensor Completion Method for
  Color Video Inpainting Problem and Fast Algorithms
Zhigang Jia Jingfei Zhu
The color video inpainting problem is one of the most challenging problem in
the modern imaging science. It aims to recover a color video from a small part
of pixels that may contain noise. However, there are less of robust models that
can simultaneously preserve the coupling of color channels and the evolution of
color video frames. In this paper, we present a new robust quaternion tensor
completion (RQTC) model to solve this challenging problem and derive the exact
recovery theory. The main idea is to build a quaternion tensor optimization
model to recover a low-rank quaternion tensor that represents the targeted
color video and a sparse quaternion tensor that represents noise. This new
model is very efficient to recover high dimensional data that satisfies the
prior low-rank assumption. To solve the case without low-rank property, we
introduce a new low-rank learning RQTC model, which rearranges similar patches
classified by a quaternion learning method into smaller tensors satisfying the
prior low-rank assumption. We also propose fast algorithms with global
convergence guarantees. In numerical experiments, the proposed methods
successfully recover color videos with eliminating color contamination and
keeping the continuity of video scenery, and their solutions are of higher
quality in terms of PSNR and SSIM values than the state-of-the-art algorithms.