to the best of our knowledge no MG method has been reported for the solution of a similar high order denoising problem which presents at the same time the challenges of dealing with nonlinearity, anisotropy, and high order derivatives. This situation is not surprising since the application of either standard linear or nonlinear MG with the typical known components does not converge. In section 5.3 we shall introduce a new nonstandard smoother for a full approximation scheme (FAS) MG algorithm.