Matlab implementations of a low-rank high-order tensor completion model, a high-order tensor RPCA model, and a hyperspectral tensor denoising method.

This code relies heavily on the following excellent studies:

[1] W. Qin, H. Wang, F. Zhang, J. Wang, X. Luo, and T. Huang, “Low-rank high-order tensor completion with applications in visual data,” IEEE Trans. Image Process., vol. 31, pp. 2433–2448, 2022.

[2] Z. Wang, J. Dong, X. Liu, and X. Zeng, “Low-rank tensor completion by approximating the tensor average rank,” in Proc. IEEE/CVF Int. Conf. Comput. Vis. (ICCV), Oct. 2021, pp. 4612–4620.

[3] C. Lu, “Transforms based tensor robust PCA: Corrupted low-rank tensors recovery via convex optimization,” in Proc. IEEE/CVF Int. Conf. Comput. Vis. (ICCV), Oct. 2021, pp. 1145–1152.

[4] S. Gu, Q. Xie, D. Meng, W. Zuo, X. Feng, and L. Zhang, “Weighted nuclear norm minimization and its applications to low level vision,” Int. J. Comput. Vis., vol. 121, no. 2, pp. 183–208, Jan. 2017.

[5] Y. Chen, W. He, N. Yokoya, T.-Z. Huang, and X.-L. Zhao, “Nonlocal tensor-ring decomposition for hyperspectral image denoising,” IEEE Trans. Geosci. Remote Sens., vol. 58, no. 2, pp. 1348–1362, Feb. 2020.

[6] L. Sun and B. Jeon, “A novel subspace spatial–spectral low rank learning method for hyperspectral denoising,” in Proc. IEEE Vis. Commun. Image Process. (VCIP), Dec. 2017, pp. 1–4.

For more information, please refer to the paper:

@article{he2024multi,
	title={Multi-Dimensional Visual Data Restoration: Uncovering the Global Discrepancy in Transformed High-Order Tensor Singular Values},
	author={He, Chengxun and Xu, Yang and Wu, Zebin and Zheng, Shangdong and Wei, Zhihui},
	journal={IEEE Trans. Image Process.}, 
	volume={33}, 
	pages={6409--6424}, 
	year={2024}, 
	publisher={IEEE}
}

I sincerely hope this trivial work is worth your precious time, if this code is helpful to you, please consider citing our work and the above inspiring studies, thank you!

Also if there is anything we can help you with, please don't hesitate to contact us.

Again, thank you for your valuable support, and we are very eager for your comment and guidance.

Chengxun He
Nanjing University of Science and Technology
E-Mail: cx.he@njust.edu.cn
WeChat: cxunhey