  In this paper, a new extrapolation economy cascadic multigrid method is
proposed to solve the image restoration model. The new method combines the new
extrapolation formula and quadratic interpolation to design a nonlinear
prolongation operator, which provides more accurate initial values for the fine
grid level. An edge preserving denoising operator is constructed to remove
noise and preserve image edges. The local smoothing operator reduces the
influence of staircase effect. The experiment results show that the new method
not only improves the computational efficiency but also ensures good recovery
quality.
