Quaternion tensor singular value decomposition using a flexible transform-based approach

Jifei Miao; Kit Ian Kou

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arXiv · 2112.08921

Quaternion tensor singular value decomposition using a flexible transform-based approach

Jifei Miao·Kit Ian Kou

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Abstract

A flexible transform-based tensor product named $\star_{{\rm{QT}}}$-product for $L$th-order ($L\geq 3$) quaternion tensors is proposed. Based on the $\star_{{\rm{QT}}}$-product, we define the corresponding singular value decomposition named TQt-SVD and the rank named TQt-rank of the $L$th-order ($L\geq 3$) quaternion tensor. Furthermore, with orthogonal quaternion transformations, the TQt-SVD can provide the best TQt-rank-$s$ approximation of any $L$th-order ($L\geq 3$) quaternion tensor. 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.

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Jifei Miao, Kit Ian Kou. 2021-12-16. Quaternion tensor singular value decomposition using a flexible transform-based approach. https://arxiv.org/abs/2112.08921

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