@article{01HMEEX27JPVPX8P2A5BP65K42,
  abstract     = {{Recently, transform-based tensor nuclear norm (TNN) methods have received increasing attention as a powerful tool for multi-dimensional visual data (color images, videos, and multispectral images, etc.) recovery. Especially, the redundant transform-based TNN achieves satisfactory recovery results, where the redundant transform along spectral mode can remarkably enhance the low-rankness of tensors. However, it suffers from expensive computational cost induced by the redundant transform. In this paper, we propose a learnable spatial-spectral transform-based TNN model for multi-dimensional visual data recovery, which not only enjoys better low-rankness capability but also allows us to design fast algorithms accompanying it. More specifically, we first project the large-scale original tensor to the small-scale intrinsic tensor via the learnable semi-orthogonal transforms along the spatial modes. Here, the semi-orthogonal transforms, serving as the key building block, can boost the spatial low-rankness and lead to a small-scale problem, which paves the way for designing fast algorithms. Secondly, to further boost the low-rankness, we apply the learnable redundant transform along the spectral mode to the small-scale intrinsic tensor. To tackle the proposed model, we apply an efficient proximal alternating minimization-based algorithm, which enjoys a theoretical convergence guarantee. Extensive experimental results on real-world data (color images, videos, and multispectral images) demonstrate that the proposed method outperforms state-of-the-art competitors in terms of evaluation metrics and running time.}},
  author       = {{Liu, Sheng and Leng, Jinsong and Zhao, Xi-Le and Zeng, Haijin and Wang, Yao and Yang, Jing-Hua}},
  issn         = {{1051-8215}},
  journal      = {{IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY}},
  keywords     = {{Tensor completion,semi-orthogonal transform,redundant transform,tensor nuclear norm,proximal alternating minimization algorithm,RANK,REPRESENTATION,DEEP,MINIMIZATION}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{3633--3646}},
  title        = {{Learnable spatial-spectral transform-based tensor nuclear norm for multi-dimensional visual data recovery}},
  url          = {{http://doi.org/10.1109/tcsvt.2023.3316279}},
  volume       = {{34}},
  year         = {{2024}},
}

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