A novel splitting method is presented for the L1-TV restoration of degraded images subject to impulsive noise. The functional is split into an L2-TV denoising part and an L1- L2 deblurring part. The dual problem of the relaxed functional is smooth with convex constraints and can be solved efficiently by applying an ArrowHurwicz-type algorithm to the augmented Lagrangian formulation. The regularization parameter is chosen automatically based on a balancing principle. The accuracy, the fast convergence, and the robustness of the algorithm and the use of the parameter choice rule are illustrated on some benchmark images and compared with an existing method.