一个基于张量火车分解的张量填充方法及在图像恢复中的应用

doi:10.15960/j.cnki.issn.1007-6093.2022.03.003

Abstract

Abstract:

Low-rank tensor completion is widely used in data recovery, and the tensor completion model based on tensor train (TT) decomposition works well in color image, video and internet data recovery. This paper proposes a tensor completion model based on the third-order tensor TT decomposition. In this model, the sparse regularization and the spatio-temporal regularization are introduced to characterize the sparsity of the kernel tensor and the inherent block similarity of the data, respectively. According to the structural characteristics of the problem, some auxiliary variables are introduced to convert the original model into a separable form equivalently, and the method of combining proximal alternating minimization (PAM) and alternating direction multiplier method (ADMM) is used to solve the model. Numerical experiments show that the introduction of two regular terms is beneficial to improve the stability and practical effect of data recovery, and the proposed method is superior to other methods. When the sampling rate is low or the image is structurally missing, the presented method is more effective.

Key words: tensor completion, tensor train (TT) decomposition, proximal alternating minimization, alternating direction method of multipliers, image restoration

CLC Number:

O221.2

Wenhui XIE, Chen LING, Chenjian PAN. A tensor completion method based on tensor train decomposition and its application in image restoration[J]. Operations Research Transactions, 2022, 26(3): 31-43.

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URL: https://www.ort.shu.edu.cn/EN/10.15960/j.cnki.issn.1007-6093.2022.03.003

https://www.ort.shu.edu.cn/EN/Y2022/V26/I3/31

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方法	SR/%
方法	3	5	7	10	15	20	25	30
TTFM	13.92	14.72	14.86	15.12	14.55	12.83	11.42	10.46
TTC-TV	3.44	4.25	4.95	6.17	8.11	10.12	12.15	14.35
HaLRTC	4.09	4.39	4.39	4.38	4.17	3.81	3.64	3.53
STDC	37.48	44.99	48.65	59.09	58.51	57.59	56.45	54.68
TNN	6.30	6.95	7.08	7.34	7.56	7.07	7.39	7.45
IpST	7.57	8.55	8.60	8.89	9.11	8.48	8.48	7.56
BCPF	137.87	130.90	121.80	137.08	138.16	141.59	146.84	157.33

方法	(5)	(6)	(7)	(8)
方法	PSNR/RSE/Time/s/Iter	PSNR/RSE/Time/s/Iter	PSNR/RSE/Time/s/Iter	PSNR/RSE/Time/s/Iter
TTFM	$ \bf{27.86}/\bf{0.13} $/8.89/42	$ \bf{35.18}/\bf{0.05} $/7.96/37	$ \bf{23.77}/\bf{0.16} $/7.95/38	$ \bf{26.28}/\bf{0.08} $/8.75/38
TTC-TV	23.16/0.22/13.27/3	31.26/0.08/43.08/3	20.85/0.22/10.46/3	24.72/0.09/35.61/3
HaLRTC	11.36/0.86/1.18/25	32.36/0.07/2.81/50	21.61/0.21/2.57/46	13.70/0.33/2.28/41
STDC	25.85/0.16/44.38/80	30.74/0.09/38.32/80	22.25/0.19/50.14/80	23.10/0.11/38.41/80
TNN	11.31/0.87/1.40/21	32.23/0.07/6.68/76	21.08/0.22/5.50/71	11.72/0.41/1.51/21
IpST	11.31/0.87/1.62/20	33.02/0.07/3.30/37	22.63/0.18/3.99/45	11.72/0.41/1.73/20
BCPF	11.30/0.87/195.41/13	28.01/0.13/177.45/12	20.66/0.23/82.79/12	11.61/0.42/156.17/11

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A tensor completion method based on tensor train decomposition and its application in image restoration

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