Learnable Spatial-Spectral Transform-Based Tensor Nuclear Norm for Multi-Dimensional Visual Data Recovery

Recently, transform-based tensor nuclear norm (TNN) methods have received increasing attention as a powerful tool for multi-dimensional visual data (color images, videos, and multispectral images, etc.) recovery. Especially, the redundant transform-based TNN achieves satisfactory recovery results, w...

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Published in:	IEEE transactions on circuits and systems for video technology Vol. 34; no. 5; pp. 3633 - 3646
Main Authors:	Liu, Sheng, Leng, Jinsong, Zhao, Xi-Le, Zeng, Haijin, Wang, Yao, Yang, Jing-Hua
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.05.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Color imagery Computational efficiency Costs Data recovery Decoding Encoding Multidimensional methods proximal alternating minimization algorithm Redundancy redundant transform semi-orthogonal transform Tensor completion tensor nuclear norm Tensors Transforms Video Videos Visualization
ISSN:	1051-8215, 1558-2205
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Abstract	Recently, transform-based tensor nuclear norm (TNN) methods have received increasing attention as a powerful tool for multi-dimensional visual data (color images, videos, and multispectral images, etc.) recovery. Especially, the redundant transform-based TNN achieves satisfactory recovery results, where the redundant transform along spectral mode can remarkably enhance the low-rankness of tensors. However, it suffers from expensive computational cost induced by the redundant transform. In this paper, we propose a learnable spatial-spectral transform-based TNN model for multi-dimensional visual data recovery, which not only enjoys better low-rankness capability but also allows us to design fast algorithms accompanying it. More specifically, we first project the large-scale original tensor to the small-scale intrinsic tensor via the learnable semi-orthogonal transforms along the spatial modes. Here, the semi-orthogonal transforms, serving as the key building block, can boost the spatial low-rankness and lead to a small-scale problem, which paves the way for designing fast algorithms. Secondly, to further boost the low-rankness, we apply the learnable redundant transform along the spectral mode to the small-scale intrinsic tensor. To tackle the proposed model, we apply an efficient proximal alternating minimization-based algorithm, which enjoys a theoretical convergence guarantee. Extensive experimental results on real-world data (color images, videos, and multispectral images) demonstrate that the proposed method outperforms state-of-the-art competitors in terms of evaluation metrics and running time.
AbstractList	Recently, transform-based tensor nuclear norm (TNN) methods have received increasing attention as a powerful tool for multi-dimensional visual data (color images, videos, and multispectral images, etc.) recovery. Especially, the redundant transform-based TNN achieves satisfactory recovery results, where the redundant transform along spectral mode can remarkably enhance the low-rankness of tensors. However, it suffers from expensive computational cost induced by the redundant transform. In this paper, we propose a learnable spatial-spectral transform-based TNN model for multi-dimensional visual data recovery, which not only enjoys better low-rankness capability but also allows us to design fast algorithms accompanying it. More specifically, we first project the large-scale original tensor to the small-scale intrinsic tensor via the learnable semi-orthogonal transforms along the spatial modes. Here, the semi-orthogonal transforms, serving as the key building block, can boost the spatial low-rankness and lead to a small-scale problem, which paves the way for designing fast algorithms. Secondly, to further boost the low-rankness, we apply the learnable redundant transform along the spectral mode to the small-scale intrinsic tensor. To tackle the proposed model, we apply an efficient proximal alternating minimization-based algorithm, which enjoys a theoretical convergence guarantee. Extensive experimental results on real-world data (color images, videos, and multispectral images) demonstrate that the proposed method outperforms state-of-the-art competitors in terms of evaluation metrics and running time.
Author	Wang, Yao Zeng, Haijin Leng, Jinsong Liu, Sheng Zhao, Xi-Le Yang, Jing-Hua
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SubjectTerms	Algorithms Color imagery Computational efficiency Costs Data recovery Decoding Encoding Multidimensional methods proximal alternating minimization algorithm Redundancy redundant transform semi-orthogonal transform Tensor completion tensor nuclear norm Tensors Transforms Video Videos Visualization
Title	Learnable Spatial-Spectral Transform-Based Tensor Nuclear Norm for Multi-Dimensional Visual Data Recovery
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