The proposed functional contains a restoration term through a regularizing function as in [3][5] for instance. This function allows an edge preservation which is not possible with a quadratic regularization. The regularizing functions used for anisotropic smoothing are usually symmetric, convex or non convex, and have at least the two following properties : a quadratic behaviour around the origin (isotropic smoothing), and sub-quadratic far from the origin (edge presevation).