  In the present work, we propose new tensor Krylov subspace method for ill
posed linear tensor problems such as in color or video image restoration. Those
methods are based on the tensor-tensor discrete cosine transform that gives
fast tensor-tensor product computations. In particular, we will focus on the
tensor discrete cosine versions of GMRES, Golub-Kahan bidiagonalisation and
LSQR methods. The presented numerical tests show that the methods are very fast
and give good accuracies when solving some linear tensor ill-posed problems.
