Weighted tensor Golub–Kahan–Tikhonov-type methods applied to image processing using a t-product

This paper discusses weighted tensor Golub–Kahan-type bidiagonalization processes using the t-product. product was introduced in M.E. Kilmer and C.D. Martin (2011). A few steps of a process with least squares norm are carried out to reduce large-scale linear discrete ill-posed problem small size. The weights determined by symmetric positive definite (SPD) tensors. Tikhonov regularization is applied reduced problem. An algorithm for Cholesky factorization SPD tensors presented. data laterally oriented matrix or general third order tensor. use Frobenius fidelity term minimization problems appropriate when noise has known covariance that not identity. We discrepancy principle determine both parameter number steps. Applications image video restoration considered.