A Single-Mode Quasi Riemannian Gradient Descent Algorithm for Low-Rank Tensor Recovery
arxiv(2024)
摘要
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.
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