Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on 2-7 Apr. 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection shows its rapid trend to further diversity and depth

Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on April 2-7, 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The vibrancy and diversity in this field are amply expressed in these important papers, and the collection clearly shows the continuing rapid growth of the use of multigrid acceleration techniques

Optimal Resolution in Maximum Entropy Image Reconstruction from Projections with Multigrid Acceleration

We consider the problem of image reconstruction from a finite number of projections over the space L 1(\Omega\Gamma1 where\Omega is a compact subset of IR 2 . We prove that, given a discretization of the projection space, the function that generates the correct projection data and maximizes the Boltzmann-Shannon entropy is piecewise constant on a certain discretization of \Omega\Gamma which we call the "optimal grid". It is on this grid that one obtains the maximum resolution given the problem setup. The size of this grid grows very quickly as the number of projections and number of cells per projection grows, indicating fast computational methods are essential to make its use feasible. We use a Fenchel duality formulation of the problem to keep the number of variables small while still using the optimal discretization, and propose a multilevel scheme to improve convergence of a simple cyclic maximization scheme applied to the dual problem. 1 Introduction In computerized tomogra..