Developing LSQR Method for Sylvester Quaternion Tensor Equations

In this paper, we consider solving a least-squares problem to the generalized Sylvester quaternion tensor equation. From the properties of quaternions and the Kronecker product, a tensor form of the LSQR algorithm is proposed for solving this problem, the convergence analysis of which is then established. Numerical results are reported to illustrate the feasibility and validity of the proposed algorithm compared with the tensor form of the CGLS method, including when the algorithm is tested with some randomly generated data and color video restoration problems.