作者 | 郑玉棒

编辑 | 陈大鑫

主要内容

 1 

研究背景

图1：被云覆盖的高光谱图像和具有元素缺失的交通数据

图2：Tucker、CP、TT和TR分解

 2 

新型张量分解：全连接张量网络分解

FCTN秩定义为由组成的向量。 

图3：FCTN分解

众所周知，矩阵分解具有转置不变性，即而对于高阶张量，论文证明了FCTN分解同样具有广义转置不变性，即

 3 

基于全连接网络分解的张量填充模型

 4 

实验结果

4.1 仿真数据实验

图4：不同缺失率下不同方法的重建结果

4.2 真实数据实验

表1：四个彩色视频在不同缺失率下所有比较方法的PSNR值和运行时间

 5 

总结

参考文献：

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[2] Kolda, T. G.; and Bader, B. W.;  Tensor Decompositions and Applications, SIAM Review, 51(3): 455-500, 2009.

[3] Oseledets, I. V.; Tensor-Train Decomposition, SIAM Journal on Scientifific Computing 33(5): 2295-2317, 2021.

[4] Zhao, Q.; Zhou, G.; Xie, S.; Zhang, L.; and Cichocki, A; Tensor Ring Decomposition, arXiv preprint arXiv:1606.05535, 2016.

[5] Liu, J.; Musialski, P.; Wonka, P.; and Ye, J.; Tensor Completion for Estimating Missing Values in Visual Data, IEEE Transactions on Pattern Analysis and Machine Intelligence 35(1): 208-220, 2013.

[6] Xu, Y.; Hao, R.; Yin, W.; and Su, Z; Parallel Matrix Factorization for Low-Rank Tensor Completion, Inverse Problems and Imaging, 9(2): 601-624, 2015.

[7] Zhang, Z.; and Aeron, S; Exact Tensor Completion Using T-SVD, IEEE Transactions on Signal Processing, 65(6): 1511-1526, 2017.

[8] Bengua, J. A.; Phien, H. N.; Tuan, H. D.; and Do, M. N.; Effificient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train, IEEE Transactions on Image Processing, 26(5): 2466-2479, 2017.

[9] Yuan, L.; Li, C.; Mandic, D.; Cao, J.; and Zhao, Q.; Tensor Ring Decomposition with Rank Minimization on Latent Space: An Effificient Approach for Tensor Completion, In Proceedings of the AAAI Conference on Artifificial Intelligence, 9151-9158, 2019.