Low-Rank Tensor Completion with Total-Variation-Regularized Transformed Tensor Schatten-p Norm for Video Inpainting

Due to the existence of missing entries in real-world tensor data, low-rank tensor completion (LRTC) problem has received increasing attention. In this paper, we propose a new transformed tensor Schatten- norm to replace the rank norm and develop a transformed multi-tensor-Schatten- norm surrogate theorem to convert the non-convex transformed tensor Schatten- norm with 0<<1 into the sum of multiple convex functions. However, tensor completion constrained by low-rank prior alone cannot protect local smoothness along the spatial and tubal dimensions. To address this drawback, we combine anisotropic total variation (TV) regularization with non-convex transformed tensor Schatten- norm with 0<<1 for LRTC. The combination of global low-rank prior and local TV prior is beneficial to improving the final completion effect. Our experimental results on grey-scale video inpainting demonstrate that our proposed method outperforms other existing state-of-the-art methods.