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Quaternion tensor singular value decomposition using a flexible transform-based approach
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DOI：10.1016/j.sigpro.2022.108910.png)
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摘要
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A flexible transform-based tensor product named *QT-product for Lth-order ( L >= 3 ) quaternion tensors is proposed. Based on the *QT-product, we define the corresponding singular value decomposition named TQt-SVD and the rank named TQt-rank of the Lth-order ( L >= 3 ) quaternion tensor. Furthermore, with orthogonal quaternion transformations, the TQt-SVD can provide the best TQt-rank-s approximation of any Lth-order ( L >= 3 ) quaternion tensor. On the other side, since a color pixel with RGB channels can be well encoded as a pure quaternion, the proposed TQt-SVD, therefore, becomes a new mathematical tool for many color image processing tasks. In the experiments, we have verified the effectiveness of the proposed TQt-SVD in the application of the best TQt-rank-s approximation for color videos represented by third-order quaternion tensors.(c) 2022 Elsevier B.V. All rights reserved.
Keyword:
Quaternion tensor singular value
decomposition
Low-rank approximation
Color image
Color video
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3.6
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10.0K
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