Low-Rank Tensor Completion by Truncated Nuclear Norm Regularization
This work addresses tensor completion for visual data recovery, presenting an incremental improvement by extending a matrix-based norm to tensors.
The paper tackled the problem of low-rank tensor completion for recovering incomplete visual data by proposing a new tensor truncated nuclear norm (T-TNN) method, which improved performance over existing methods as demonstrated in experiments on real-world videos and images.
Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have suggested several definitions of tensor nuclear norm. However, they have limitations and may not properly approximate the real rank of a tensor. Besides, they do not explicitly use the low-rank property in optimization. It is proved that the recently proposed truncated nuclear norm (TNN) can replace the traditional nuclear norm, as a better estimation to the rank of a matrix. Thus, this paper presents a new method called the tensor truncated nuclear norm (T-TNN), which proposes a new definition of tensor nuclear norm and extends the truncated nuclear norm from the matrix case to the tensor case. Beneficial from the low rankness of TNN, our approach improves the efficacy of tensor completion. We exploit the previously proposed tensor singular value decomposition and the alternating direction method of multipliers in optimization. Extensive experiments on real-world videos and images demonstrate that the performance of our approach is superior to those of existing methods.