A subspace-orbit randomized algorithm for quaternion tensor singular value decomposition based on Qt-product - Liu, Yonghe; Wu, Fengsheng; Miao, Jifei; Li, Chaoqian (Applied mathematics and computation, 2026)
•We investigate the third-order quaternion tensor singular value decomposition.•We propose a subspace-orbit randomized algorithm based on block Krylov iteration.•This algorithm can achieve the trade-off between computation time and accuracy.•We provide the deterministic and expected approximation error bounds.•This algorithm is applied to color video compression and denoising.. Based on a subspace-orbit random projection method and a randomized block Krylov iteration approach, we propose a subspace-orbit randomized algorithm with the block Krylov iteration for third-order quaternion tensor singular value decomposition based on Qt-product. The deterministic and expected approximation error bounds for the proposed randomized algorithm are given. Numerical experiments using synthetic data and color video data are presented to demonstrate its feasibility and effectiveness.