2024/01/29 by Yuanwei Zhang, Yanan Zhu, Zhang, Yuanwei +3
Earth and Planetary Sciences · Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #Seismic Imaging and Inversion Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2401.15925
openalex publication_date 2024/01/29 · openalex created_date 2024/01/31 · openalex updated_date 2026/07/28
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.