Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation

Abstract

Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing randomized techniques are first devised under the order-d (d >= 3) T-SVD framework. On this basis, we then further investigate the robust high-order tensor completion (RHTC) problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. To the best of our knowledge, this is the first study to incorporate the randomized low-rank approximation into the RHTC problem. Empirical studies on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision.