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The application of tensor ring and tensor train completion to image recovery | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 19، دوره 14، شماره 3، خرداد 2023، صفحه 223-230 اصل مقاله (1.26 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.24206.2688 | ||
| نویسندگان | ||
| Hamid Reza Yazdani* 1؛ Alireza Shojaeifard1؛ Mohsen Sahrezai2 | ||
| 1Department of Mathematics, Faculty of Basic Sciences, Imam Hossein Comprehensive University, Tehran, Iran | ||
| 2Faculty of Defense and Engineering, Imam Hossein University, Tehran, Iran | ||
| تاریخ دریافت: 19 مرداد 1400، تاریخ پذیرش: 15 شهریور 1401 | ||
| چکیده | ||
| Tensor completion has numerous applications in digital image processing such as image recovery and video overlay. In this paper, we consider two new approaches to tensor completion. Efficient low-rank tensor with tensor train and tensor ring for image recovery, some basic concepts about tensor algebra and completion problems are presented, after that Tensor completion based on the tensor train and tensor ring are offered and implemented on some examples for image recovery with different observed ratios. The results of these implementations are compared and final results are proposed. | ||
| کلیدواژهها | ||
| Image Recovery؛ Tensor Completion (TC)؛ Tensor Ring (TR)؛ Tensor Train (TT) | ||
| مراجع | ||
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[1] A. Cichocki, D. Mandic, L. De Lathauwer, G. Zhou, Q. Zhao, C. Caiafa and H. A. Phan, Tensor decompositions for signal processing applications: From two-way to multi-way component analysis, IEEE Signal Process. Mag. 32 (2015), no. 2, 145—163.
[2] E.J. Candes and B. Recht, Exact matrix completion via convex optimization, Commun. ACM 55 (2012), no. 6, 111–119.
[3] T. Kolda and B. Bader. Tensor decompositions and applications, SIAM Rev. 51 (2009), no. 3, 455-–500.
[4] M. Kurucz, A. Benczur and K. Csalogany, Methods for large scale svd with missing values, Proc. KDD Cup Workshop, San Jos´e, USA: Citeseer, 2007, vol. 12.
[5] J. Liu, P. Musialski , P. Wonka, and Ye J., Tensor completion for estimating missing values in visual data, IEEE Trans. Pattern Anal. Machine Intel. 35 (2012), no. 1, 208–220.
[6] R. Orus, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Ann. Phys. 349 (2014), 117—158.
[7] I. V. Oseledets. Tensor train decomposition, SIAM J. Sci. Comput. 33 (2011), no. 5, 2295-–23171.
[8] L. Qi, The spectral theory of tensors, In textitarXiv: 1201.3424v1 (2012).
[9] Q. Song, H. Ge, J. Caverlee and X. Hu, Tensor completion algorithms in big data analytics, ACM Trans. Knowledge Disc. Data, 6 (2019), no. 13, 1—48.
[10] W. Wang, V. Aggrawal and S. Aeron, Efficient low rank tensor ring completion, IEEE Int. Conf. Comput. Vision (ICCV), 2017, pp. 5697–5705.
[11] Q. Zhao, G. Zhou, S. Xie, L. Zhang and A. Cichocki, Tensor ring decomposition, arXiv preprint arXiv:1606.05535 (2016). | ||
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