Matrix Krylov subspace methods for image restoration

In the present paper, we consider some matrix Krylov subspace methods for solving ill-posed linear matrix equations and in those problems coming from the restoration of blurred and noisy images. Applying the well known Tikhonov regularization procedure leads to a Sylvester matrix equation depending the Tikhonov regularized parameter. We apply the matrix versions of the well known Krylov subspace methods, namely the Least Squared (LSQR) and the conjugate gradient (CG) methods to get approximate solutions representing the restored images. Some numerical tests are presented to show the effectiveness of the proposed methods.