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<p>Recently, the tensor recovery problem has witnessed significant advancements with the non-convex relaxation methods, compared with convex relaxation methods. In this article, we propose a novel non-convex relaxation method for the low-rank tensor completion and tensor robust principal component analysis, which uses the global low-rankness and local smoothness of the recovered tensor. And we further build the solving algorithms of the proposed models based on the well-known ADMM and the linear approximation method. The better performance of our proposed method is unequivocally validated by extensive numerical experiments, compared to other state-of-the-art methods in terms of both numerical accuracy and visual quality. We further propose ADMM algorithms with fine convergence to solve the proposed models.</p>

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A Non-convex Regularization Fusing Low-rankness and Smoothness for Tensor Recovery

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • Huanmin Ge,
  • Yue Zhang,
  • Michael K. Ng

摘要

Recently, the tensor recovery problem has witnessed significant advancements with the non-convex relaxation methods, compared with convex relaxation methods. In this article, we propose a novel non-convex relaxation method for the low-rank tensor completion and tensor robust principal component analysis, which uses the global low-rankness and local smoothness of the recovered tensor. And we further build the solving algorithms of the proposed models based on the well-known ADMM and the linear approximation method. The better performance of our proposed method is unequivocally validated by extensive numerical experiments, compared to other state-of-the-art methods in terms of both numerical accuracy and visual quality. We further propose ADMM algorithms with fine convergence to solve the proposed models.