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<p>The recently proposed tensor wheel (TW) decomposition has great potential in handling high-order data recovery tasks. TW decomposition consists of a core factor and <i>N</i> ring factors, using a new wheel topology to characterize complex interactions in multi-dimensional tensors. However, the performance of the TW network will decline when the rank is inaccurately estimated, which requires an appropriate TW rank to maintain good performance. In this paper, we impose a factor-based regularization to formulate a novel TW decomposition-based tensor completion model that could keep the rank robustness and further yield stable performance. Furthermore, equipped with an efficient proximal alternating minimization-based solving algorithm with guaranteed convergence, we can solve the proposed tensor completion model and prove its convergence in theory. Experiments on a large amount of synthetic and real data show that the proposed method achieves competitive outcomes compared with the classic and latest methods, effectively reducing the burden of TW rank selection, and the results are more stable. For example, for a sampling rate of 5%, we obtain an average PSNR gain of about 2 db on 19 images. Moreover, on the MSI image <i>Toy</i>, for different rank selections, the proposed method outperforms the TW method across different rank selections, achieving excellent rates of 100%/91%/64%. These experimental results demonstrate the effectiveness and robustness of the proposed method.</p>

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A Robust Tensor Wheel Decomposition-Based Regularization Method for Tensor Completion Problem

  • 期刊论文

  • 发表日期：

    2025年5月19日

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  • Xiao Wu,
  • Ting-Zhu Huang,
  • Zhong-Cheng Wu,
  • Liang-Jian Deng

摘要

The recently proposed tensor wheel (TW) decomposition has great potential in handling high-order data recovery tasks. TW decomposition consists of a core factor and N ring factors, using a new wheel topology to characterize complex interactions in multi-dimensional tensors. However, the performance of the TW network will decline when the rank is inaccurately estimated, which requires an appropriate TW rank to maintain good performance. In this paper, we impose a factor-based regularization to formulate a novel TW decomposition-based tensor completion model that could keep the rank robustness and further yield stable performance. Furthermore, equipped with an efficient proximal alternating minimization-based solving algorithm with guaranteed convergence, we can solve the proposed tensor completion model and prove its convergence in theory. Experiments on a large amount of synthetic and real data show that the proposed method achieves competitive outcomes compared with the classic and latest methods, effectively reducing the burden of TW rank selection, and the results are more stable. For example, for a sampling rate of 5%, we obtain an average PSNR gain of about 2 db on 19 images. Moreover, on the MSI image Toy, for different rank selections, the proposed method outperforms the TW method across different rank selections, achieving excellent rates of 100%/91%/64%. These experimental results demonstrate the effectiveness and robustness of the proposed method.