  The present paper is concerned with developing tensor iterative Krylov
subspace methods to solve large multi-linear tensor equations. We use the
well-known T-product for two tensors to define tensor global Arnoldi and tensor
global Gloub-Kahan bidiagonalization algorithms. Furthermore, we illustrate how
tensor-based global approaches can be exploited to solve ill-posed problems
arising from recovering blurry multichannel (color) images and videos, using
the so-called Tikhonov regularization technique, to provide computable
approximate regularized solutions. We also review a generalized
cross-validation and discrepancy principle type of criterion for the selection
of the regularization parameter in the Tikhonov regularization. Applications to
RGB image and video processing are given to demonstrate the efficiency of the
algorithms.
