Low-Rank Tensor Completion Based on Self-Adaptive Learnable Transforms

Wu, Tongle, Gao, Bin, Fan, Jicong, Xue, Jize and Woo, Wai Lok (2022) Low-Rank Tensor Completion Based on Self-Adaptive Learnable Transforms. IEEE Transactions on Neural Networks and Learning Systems. pp. 1-13. ISSN 2162-237X (In Press)

Low-Rank Tensor Completion Based on Self-Adaptive Learnable Transforms.pdf - Accepted Version

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Official URL: https://doi.org/10.1109/tnnls.2022.3215974


The tensor nuclear norm (TNN), defined as the sum of nuclear norms of frontal slices of the tensor in a frequency domain, has been found useful in solving low-rank tensor recovery problems. Existing TNN-based methods use either fixed or data-independent transformations, which may not be the optimal choices for the given tensors. As the consequence, these methods cannot exploit the potential low-rank structure of tensor data adaptively. In this article, we propose a framework called self-adaptive learnable transform (SALT) to learn a transformation matrix from the given tensor. Specifically, SALT aims to learn a lossless transformation that induces a lower average-rank tensor, where the Schatten- p quasi-norm is used as the rank proxy. Then, because SALT is less sensitive to the orientation, we generalize SALT to other dimensions of tensor (SALTS), namely, learning three self-adaptive transformation matrices simultaneously from given tensor. SALTS is able to adaptively exploit the potential low-rank structures in all directions. We provide a unified optimization framework based on alternating direction multiplier method for SALTS model and theoretically prove the weak convergence property of the proposed algorithm. Experimental results in hyperspectral image (HSI), color video, magnetic resonance imaging (MRI), and COIL-20 datasets show that SALTS is much more accurate in tensor completion than existing methods. The demo code can be found at https://faculty.uestc.edu.cn/gaobin/zh_ CN/lwcg/153392/list/index.htm.

Item Type: Article
Additional Information: Funding information: This work was supported in part by the National Natural Science Foundation of China under Grant 61971093, Grant 61960206010, and Grant 61527803; in part by the NSFC Projects of International Cooperation and Exchanges under Grant 61960206010; in part by the International Science and Technology Innovation Cooperation Project of Sichuan Province under Grant 2021YFH0036; in part by the Fundamental Research Funds for the Central Universities under Grant ZYGX2019J067; in part by the Shenzhen Research Institute of Big Data under Grant T00120210002; and in part by the Youth Program of the National Natural Science Foundation of China under 62106211.
Uncontrolled Keywords: Discrete Fourier transforms, Frequency-domain analysis, Learnable transform, Learning systems, Matrix decomposition, Optimization, Tensors, Transforms, low-rank, self-adaptive, tensor completion
Subjects: G400 Computer Science
G500 Information Systems
G600 Software Engineering
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Elena Carlaw
Date Deposited: 16 Dec 2022 15:56
Last Modified: 16 Dec 2022 16:00
URI: https://nrl.northumbria.ac.uk/id/eprint/50927

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