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

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

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Abstract

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.

Zusammenfassung

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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References

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  1. Seminar für Angewandte Mathematik, Eidgenössische Technische Hochschule, CH-8092, Zürich, Switzerland

    M. R. Trummer

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  1. M. R. Trummer
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Trummer, M.R. Reconstructing pictures from projections: On the convergence of the ART algorithm with relaxation. Computing 26, 189–195 (1981). https://doi.org/10.1007/BF02243477

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  • DOI: https://doi.org/10.1007/BF02243477

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