Numerical Methods in Tomography

Frank Natterer

Institut für Numerische
und instrumentelle Mathematik
Universität Münster
Einsteinstrasse 62
D-48149 Münster, Germany
E-mail: nattere@math.uni-muenster.de

• Contents
• Introduction
  • The basic example
  • An annotated bibliography
  • Outline of the paper
  • Prerequisites
• The filtered backprojection algorithm
  • Parallel geometry in the plane
  • The interlaced parallel geometry
  • Standard fan beam geometry
  • Linear fan beam geometry
  • Fast backprojection
• 3D reconstruction formulas
  • Inversion of the 3D Radon transform
  • The FDK approximate formula
  • Grangeat's formula
  • Orlov's inversion formula
  • Colsher's inversion formula
  • Conical tilt geometry
• Iterative methods
  • ART (algebraic reconstruction technique)
  • EM (expectation maximation)
  • MART (multiplicative algebraic reconstruction technique)
• Circular harmonic algorithms
• Fourier reconstruction
• Outlook
• References
• About this document ...