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 ...

In this article we review the image reconstruction algorithms used in tomography. We restrict ourselves to the standard problems in the reconstruction of function from line or plane integrals as they occur in X-ray tomography, nuclear medicine, magnetic resonance imaging, and electron microscopy. Non-standard situations, such as incomplete data, unknown orientations, local tomography, discrete tomography are not dealt with. Nor do we treat nonlinear tomographic techniques such as impedance, ultrasound, and near infrared imaging.