A Single-Mode Quasi Riemannian Gradient Descent Algorithm for Low-Rank Tensor Recovery

Abstract: This paper focuses on recovering a low-rank tensor from its incomplete measurements. We propose a novel algorithm termed the Single Mode Quasi Riemannian Gradient Descent (SM-QRGD). By exploiting the benefits of both fixed-rank matrix tangent space projection in Riemannian gradient descent and sequentially truncated high-order singular value decomposition (ST-HOSVD), SM-QRGD achieves a much faster convergence speed than existing state-of-the-art algorithms. Theoretically, we establish the convergence of SM-QRGD through the Tensor Restricted Isometry Property (TRIP) and the geometry of the fixed-rank matrix manifold. Numerically, extensive experiments are conducted, affirming the accuracy and efficacy of the proposed algorithm.