Application of multigrid techniques to image restoration problems

We briefly describe a multigrid strategy for unilevel and two-level linear systems whose coefficient matrix A(n) belongs either to the Toeplitz class or to the cosine algebra of type III and such that A(n) can be naturally associated, in the spectral sense, with a polynomial function f. The interest of the technique is due to its optimal cost of O(N) arithmetic operations, where N is the size of the algebraic problem. We remark that these structures arise in certain 2D image restoration problems or can be used as preconditioners for more complicated image restoration problems.