Non-convex approaches for low-rank tensor completion under tubal sampling
This work addresses tensor completion for data analysis, but it appears incremental as it builds on existing sampling strategies and methods.
The authors tackled the problem of tensor completion under tubal sampling by proposing two non-convex methods, TL12 and TCCUR, which showed a trade-off between accuracy and time efficiency in low sampling ratios, outperforming classical methods in at least one aspect.
Tensor completion is an important problem in modern data analysis. In this work, we investigate a specific sampling strategy, referred to as tubal sampling. We propose two novel non-convex tensor completion frameworks that are easy to implement, named tensor $L_1$-$L_2$ (TL12) and tensor completion via CUR (TCCUR). We test the efficiency of both methods on synthetic data and a color image inpainting problem. Empirical results reveal a trade-off between the accuracy and time efficiency of these two methods in a low sampling ratio. Each of them outperforms some classical completion methods in at least one aspect.