DocServer

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

Limber, Mark A. and Manteuffel, Tom A. and McCormick, Stephen F. (1993) Optimal Resolution in Maximum Entropy Image Reconstruction from Projections with Multigrid Acceleration. [Preprint]

[img]
Preview
Postscript
Download (520Kb) | Preview
    [img]
    Preview
    PDF
    Download (278Kb) | Preview

      Abstract

      We consider the problem of image reconstruction from a finite number of projections over the space $L^1(\Omega)$, where $\Omega$ is a compact subset of $\Reals^2$. 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 $\Omega$, 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.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Subjects: UNSPECIFIED
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 17 Nov 2003
      Last Modified: 21 Apr 2010 11:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/63

      Actions (login required)

      View Item