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

•A flexible transform-based tensor product named *QT-product for Lth-order (L≥3) quaternion tensors is proposed.•Following the ?QT-product, a quaternion tensor singular value decomposition named TQt-SVD for Lth-order (L≥3) quaternion tensors is defined.•Based on the defined TQt-SVD, a rank named TQt-rank of Lth-order (L≥3) quaternion tensors is defined, which can well characterize the low rankness of color videos.