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Applied Mathematics & Optimization

, Volume 75, Issue 1, pp 55–73 | Cite as

Tomographic Reconstruction from a Few Views: A Multi-Marginal Optimal Transport Approach

  • I. Abraham
  • R. Abraham
  • M. BergouniouxEmail author
  • G. Carlier
Article

Abstract

In this article, we focus on tomographic reconstruction. The problem is to determine the shape of the interior interface using a tomographic approach while very few X-ray radiographs are performed. We use a multi-marginal optimal transport approach. Preliminary numerical results are presented.

Keywords

Tomographic reconstruction Multi-marginal optimal transport Variational method Inverse problem Optimization 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • I. Abraham
    • 1
  • R. Abraham
    • 2
  • M. Bergounioux
    • 2
    Email author
  • G. Carlier
    • 3
  1. 1.CEA Ile de FranceBruyères le ChâtelFrance
  2. 2.Université d’Orléans, UFR Sciences, MAPMO, UMR 7349Orléans Cedex 2France
  3. 3.CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, Pl. de Lattre de TassignyParis Cedex 16France

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