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Variational Methods for Tomographic Reconstruction with Few Views

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Abstract

We deal with a severe ill posed problem, namely the reconstruction process of an image during tomography acquisition with (very) few views. We present different methods that we have been investigated during the past decade. They are based on variational analysis. This is a survey paper and we refer to the quoted papers for more details.

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Authors and Affiliations

  1. Institut Denis Poisson – UMR 7013, Université d’Orléans, BP 6759, F-45067, Orléans Cedex 2, France

    Maïtine Bergounioux & Romain Abraham

  2. CEA Ile de France, BP 12, 91680, Bruyères le Châtel, France

    Isabelle Abraham

  3. CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, Pl. de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Guillaume Carlier

  4. CMAP, École polytechnique, CNRS, Université Paris-Saclay, 91128, Palaiseau, France

    Erwan Le Pennec

  5. Laboratoire Jacques-Louis Lions, CNRS Inria, équipe CAGE, Sorbonne Université (Paris 6), 4 place Jussieu BC 187, 75252, Paris cedex 05, France

    Emmanuel Trélat

Authors
  1. Maïtine Bergounioux
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  2. Isabelle Abraham
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  3. Romain Abraham
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  4. Guillaume Carlier
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  5. Erwan Le Pennec
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  6. Emmanuel Trélat
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Corresponding author

Correspondence to Maïtine Bergounioux.

Additional information

Lecture delivered at the Seminario Matematico e Fisico di Milano on January 15, 2018

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Bergounioux, M., Abraham, I., Abraham, R. et al. Variational Methods for Tomographic Reconstruction with Few Views. Milan J. Math. 86, 157–200 (2018). https://doi.org/10.1007/s00032-018-0285-1

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  • DOI: https://doi.org/10.1007/s00032-018-0285-1

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