Title: The Twist Tensor Nuclear Norm for Video Completion
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| Authors: Hu, WR; Tao, DC; Zhang, WS; Xie, Y; Yang, YH
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| Author Full Names: Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui
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| Source: IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 28 (12):2961-2973; 10.1109/TNNLS.2016.2611525 DEC 2017
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| Language: English
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| Abstract: In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.
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| ISSN: 2162-237X
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| eISSN: 2162-2388
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| IDS Number: FN8GR
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| Unique ID: WOS:000416261400010
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| PubMed ID: 27705868
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