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<p>By decomposing a third-order tensor into three factor tensors, we propose a low-rank regularized tensor completion model for recovering multi-dimensional image data. To address the optimization challenges, we construct a Riemannian metric on the search space that incorporates preconditioning techniques, thereby embedding second-order information into the geometry of the manifold. Based on this framework, we develop Riemannian gradient descent (RPGD) and Riemannian conjugate gradient (RPCG) algorithms, equipped with Armijo line search and Riemannian Barzilai-Borwein step size initialization. Under standard assumptions, we rigorously establish the global convergence of both algorithms. Numerical experiments on color images, face images, and multispectral data demonstrate that our methods outperform state-of-the-art approaches in both recovery accuracy and computational efficiency.</p>

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Riemannian Preconditioning Algorithms for the Low-Rank Tensor Completion via the Triple Decomposition

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Yaqiong Wen,
  • Wen Li,
  • Jiakai Chen,
  • Yannan Chen

摘要

By decomposing a third-order tensor into three factor tensors, we propose a low-rank regularized tensor completion model for recovering multi-dimensional image data. To address the optimization challenges, we construct a Riemannian metric on the search space that incorporates preconditioning techniques, thereby embedding second-order information into the geometry of the manifold. Based on this framework, we develop Riemannian gradient descent (RPGD) and Riemannian conjugate gradient (RPCG) algorithms, equipped with Armijo line search and Riemannian Barzilai-Borwein step size initialization. Under standard assumptions, we rigorously establish the global convergence of both algorithms. Numerical experiments on color images, face images, and multispectral data demonstrate that our methods outperform state-of-the-art approaches in both recovery accuracy and computational efficiency.