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

12/16/2021

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by   Jifei Miao, et al.

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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. 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.