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Projection Methods for Uniformly Convex Expandable Sets

Author

Listed:
  • Stéphane Chrétien

    (Laboratoire ERIC, Université Lyon 2, 69500 Bron, France
    The Alan Turing Institute, London NW1 2DB, UK
    Data Science Division, The National Physical Laboratory, Teddington TW11 0LW, UK)

  • Pascal Bondon

    (Laboratoire des Signaux et Systèmes, CentraleSupélec, CNRS, Université Paris-Saclay, 91190 Gif-sur-Yvette, France)

Abstract

Many problems in medical image reconstruction and machine learning can be formulated as nonconvex set theoretic feasibility problems. Among efficient methods that can be put to work in practice, successive projection algorithms have received a lot of attention in the case of convex constraint sets. In the present work, we provide a theoretical study of a general projection method in the case where the constraint sets are nonconvex and satisfy some other structural properties. We apply our algorithm to image recovery in magnetic resonance imaging (MRI) and to a signal denoising in the spirit of Cadzow’s method.

Suggested Citation

  • Stéphane Chrétien & Pascal Bondon, 2020. "Projection Methods for Uniformly Convex Expandable Sets," Mathematics, MDPI, vol. 8(7), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1108-:d:380849
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    References listed on IDEAS

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    1. Yair Censor & Wei Chen & Patrick Combettes & Ran Davidi & Gabor Herman, 2012. "On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints," Computational Optimization and Applications, Springer, vol. 51(3), pages 1065-1088, April.
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