, Volume 26, Issue 3, pp 189–195

Reconstructing pictures from projections: On the convergence of the ART algorithm with relaxation

  • M. R. Trummer


The convergence of the additive and linear ART algorithm with relaxation is proved in a new way and under weaker assumptions on the sequence of the relaation parameters than in earlier works. These algorithms are iterative methods for the reconstruction of digitized pictures from one-dimesional views. A second proof using elementary matrix algebra shows the geometric convergence of the linear ART algorithm with relaxation.

Über die Konvergenz des ART-Algorithmus für die Rekonstruktion von Bildern


ART-Algorithmen sind iterative Methoden zur Rekonstruktion von digitalen Bildern aus ihren Projektionen. Die Konvergenz des additiven und linearen (nicht restringierten) ART-Algorithmus mit Relaxation wird unter weit schwächeren Voraussetzungen über die Relaxationsparameter als bei bisher bekannten Resultaten bewiesen. Ein anderer Beweis zeigt die geometrisch schnelle Konvergenz des linearen relaxierten ART-Algorithmus.


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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • M. R. Trummer
    • 1
  1. 1.Seminar für Angewandte MathematikEidgenössische Technische HochschuleZürichSwitzerland

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