Discrete cosine transform LSQR methods for multidimensional ill-posed problems

We propose new tensor krylov subspace methods for ill-posed linear tensor problems such as 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.