Tensor-Ring Nuclear Norm Minimization and Application for Visual Data Completion
This work addresses computational inefficiencies and rank determination challenges in tensor-based visual data completion, offering a more efficient solution for applications like image and video restoration.
The paper tackles the problem of visual data completion by introducing a new tensor nuclear norm based on tensor circular unfolding, which overcomes non-convexity and computational demands of existing tensor ring methods, and demonstrates superior performance in image/video in-painting with striped missing values.
Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally demanding. In addition, the determination of the optimal TR rank is a tough work in practice. To overcome these drawbacks, we first introduce a class of new tensor nuclear norms by using tensor circular unfolding. Then we theoretically establish connection between the rank of the circularly-unfolded matrices and the TR ranks. We also develop an efficient tensor completion algorithm by minimizing the proposed tensor nuclear norm. Extensive experimental results demonstrate that our proposed tensor completion method outperforms the conventional tensor completion methods in the image/video in-painting problem with striped missing values.