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Algorithms 2018, 11(7), 94; https://doi.org/10.3390/a11070094

Tensor Completion Based on Triple Tubal Nuclear Norm

1
School of Physics and Electronic Electrical Engineering, Huaiyin Normal University, Huaian 223300, China
2
School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
3
Jiangsu Province Key Construction Laboratory of Modern Measurement Technology and Intelligent System, Huaian 223300, China
4
School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
5
Jiangsu Yaoshi Software Technology Co., Ltd., Nanjing 211103, China
6
Jiangsu Shuoshi Welding Technology Co., Ltd., Nanjing 211103, China
*
Author to whom correspondence should be addressed.
Received: 21 May 2018 / Revised: 16 June 2018 / Accepted: 19 June 2018 / Published: 28 June 2018
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Abstract

Many tasks in computer vision suffer from missing values in tensor data, i.e., multi-way data array. The recently proposed tensor tubal nuclear norm (TNN) has shown superiority in imputing missing values in 3D visual data, like color images and videos. However, by interpreting in a circulant way, TNN only exploits tube (often carrying temporal/channel information) redundancy in a circulant way while preserving the row and column (often carrying spatial information) relationship. In this paper, a new tensor norm named the triple tubal nuclear norm (TriTNN) is proposed to simultaneously exploit tube, row and column redundancy in a circulant way by using a weighted sum of three TNNs. Thus, more spatial-temporal information can be mined. Further, a TriTNN-based tensor completion model with an ADMM solver is developed. Experiments on color images, videos and LiDAR datasets show the superiority of the proposed TriTNN against state-of-the-art nuclear norm-based tensor norms. View Full-Text
Keywords: tensor completion; tensor SVD; ADMM; image inpainting; video inpainting tensor completion; tensor SVD; ADMM; image inpainting; video inpainting
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Wei, D.; Wang, A.; Feng, X.; Wang, B.; Wang, B. Tensor Completion Based on Triple Tubal Nuclear Norm. Algorithms 2018, 11, 94.

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