Paige’s Algorithm for solving a class of tensor least squares problem

In this paper, we consider a class of tensor least squares problem with an invertible linear transform, which arises in image restoration. Based on the operator-bidiagonal procedure, two Paige’s algorithms are designed to solve it. The convergence theorems of the new methods are derived. Numerical experiments are performed to illustrate the feasibility and efficiency of the new methods, including when the algorithm is tested with the synthetic data and on some image restoration problems. Comparisons with some previous methods are also given.