tproduct: Tensor-Tensor Product Toolbox. The tensor-tensor product (t-product) [1] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD (see an illustration in the figure below), tensor spectral norm, tensor nuclear norm [2] and many others. The linear algebraic structure of tensors are similar to the matrix cases. We develop a Matlab toolbox to implement several basic operations on tensors based on t-product.

References in zbMATH (referenced in 23 articles )

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  1. Bentbib, A. H.; Hachimi, A. El; Jbilou, K.; Ratnani, A.: A tensor regularized nuclear norm method for image and video completion (2022)
  2. Reichel, Lothar; Ugwu, Ugochukwu O.: Tensor Arnoldi-Tikhonov and GMRES-type methods for ill-posed problems with a t-product structure (2022)
  3. Beik, F. P. A.; El Ichi, A.; Jbilou, K.; Sadaka, R.: Tensor extrapolation methods with applications (2021)
  4. Chen, Jinchi; Gao, Weiguo; Wei, Ke: Exact matrix completion based on low rank Hankel structure in the Fourier domain (2021)
  5. Chen, Lixia; Liu, Junli; Wang, Xuewen: Background subtraction with Kronecker-basis-representation based tensor sparsity and (l_1,1,2) norm (2021)
  6. Chen, Xuemei; Qin, Jing: Regularized Kaczmarz algorithms for tensor recovery (2021)
  7. Hou, Jingyao; Zhang, Feng; Wang, Jianjun: One-bit tensor completion via transformed tensor singular value decomposition (2021)
  8. Kong, Hao; Lu, Canyi; Lin, Zhouchen: Tensor Q-rank: new data dependent definition of tensor rank (2021)
  9. Liang, Peidong; Likassa, Habte Tadesse; Zhang, Chentao; Guo, Jielong: New robust PCA for outliers and heavy sparse noises’ detection via affine transformation, the (L_\ast, w) and (L_2,1) norms, and spatial weight matrix in high-dimensional images: from the perspective of signal processing (2021)
  10. Li, Minghui; Li, Wen; Chen, Yannan; Xiao, Mingqing: The nonconvex tensor robust principal component analysis approximation model via the weighted (\ell_p)-norm regularization (2021)
  11. Li, Xia; Wang, Yong; Huang, Zheng-Hai: Continuity, differentiability and semismoothness of generalized tensor functions (2021)
  12. Qiu, Duo; Bai, Minru; Ng, Michael K.; Zhang, Xiongjun: Robust low transformed multi-rank tensor methods for image alignment (2021)
  13. Qiu, Duo; Bai, Minru; Ng, Michael K.; Zhang, Xiongjun: Nonlocal robust tensor recovery with nonconvex regularization (2021)
  14. Zheng, Meng-Meng; Huang, Zheng-Hai; Wang, Yong: T-positive semidefiniteness of third-order symmetric tensors and T-semidefinite programming (2021)
  15. Chapel, Marie-Neige; Bouwmans, Thierry: Moving objects detection with a moving camera: a comprehensive review (2020)
  16. Jiang, Tai-Xiang; Huang, Ting-Zhu; Zhao, Xi-Le; Deng, Liang-Jian: Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm (2020)
  17. Likassa, Habte Tadesse; Xian, Wen; Tang, Xuan: New robust regularized shrinkage regression for high-dimensional image recovery and alignment via affine transformation and Tikhonov regularization (2020)
  18. Wang, Xuezhong; Che, Maolin; Wei, Yimin: Tensor neural network models for tensor singular value decompositions (2020)
  19. Yang, Jing-Hua; Zhao, Xi-Le; Ma, Tian-Hui; Ding, Meng; Huang, Ting-Zhu: Tensor train rank minimization with hybrid smoothness regularization for visual data recovery (2020)
  20. Yang, Ming; Luo, Qilun; Li, Wen; Xiao, Mingqing: Multiview clustering of images with tensor rank minimization via nonconvex approach (2020)

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