Image restoration using multigrid methods

In this paper, we discuss several iterative methods for solving the system of linear equations that arises in the process of solving a Fredholm integral equation of the first kind. When applied to the very large systems that arise in connection with two- or three-dimension signal reconstructions, direct methods based on the singular-value decomposition require too much computation and conventional single grid iterative schemes may converge too slowly. We have developed a multigrid scheme in which the solution is sought on a fine grid, but discretizations on a set of coarser grids are used for intermediate calculations to reduce the overall computation effort. Although the quality of the reconstruction obtained using such methods is typically not as good as that achieved using a singular-value decomposition based method, computational considerations should make multigrid methods appealing for large systems of equations.