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. Based on the ★QT-product, we define corresponding singular value decomposition TQt-SVD and rank TQt-rank of tensor. Furthermore, with orthogonal transformations, can provide best TQt-rank-s approximation any On other side, since a color pixel RGB channels be well encoded as pure quaternion, proposed TQt-SVD, therefore, becomes new mathematical tool many image processing tasks. In experiments, have verified effectiveness in application videos represented by third-order tensors.