Tensor Regularized Total Least Squares Methods with Applications to Image and Video Deblurring

Total Least Squares (TLS) is an effective method for solving linear equations with the situations, when noise is not just in observation matrices but also mapping matrices. Moreover, Tikhonov regularization is widely used in plenty of ill-posed problems. In this paper, we extend the Regularized Total Least Squares (RTLS) method in matrix form proposed by Golub, Hansen and O'Leary in 1999 to tensor form, proposing the tensor Regularized Total Least Squares (TRTLS) method for solving ill-conditioned tensor systems of equations. Properties and algorithms about the solution of TRTLS problem, which might be similar with those about RTLS, are also proposed and proved. Based on this method, some applications in image and video deblurring are explored in this paper. Numerical experiments show the effectiveness of TRTLS method, compared with the existing methods.