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Fast inversion of the Radon transform using log-polar coordinates and partial back-projections

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Author

  • Fredrik Andersson

Summary, in English

In this paper a novel filtered back-projection algorithm for inversion of a discretized Radon transform is presented. It makes use of invariance properties possessed by both the Radon transform and its dual. By switching to log-polar coordinates, both operators can be expressed in a displacement invariant manner. Explicit expressions for the corresponding transfer functions are calculated. Furthermore, by dividing the back-projection into several partial back-projections, inversion can be performed by means of finite convolutions and hence implemented by an FFT-algorithm. In this way, a fast and accurate reconstruction method is obtained.

Publishing year

2005

Language

English

Pages

818-837

Publication/Series

SIAM Journal on Applied Mathematics

Volume

65

Issue

3

Document type

Journal article

Publisher

Society for Industrial and Applied Mathematics

Topic

  • Mathematics

Keywords

  • Radon transform
  • filtered back-projection

Status

Published

Research group

  • Harmonic Analysis and Applications

ISBN/ISSN/Other

  • ISSN: 0036-1399