Projection Methods for Uniformly Convex Expandable Sets

Stéphane Chrétien and Pascal Bondon
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Stéphane Chrétien: Laboratoire ERIC, Université Lyon 2, 69500 Bron, France
Pascal Bondon: Laboratoire des Signaux et Systèmes, CentraleSupélec, CNRS, Université Paris-Saclay, 91190 Gif-sur-Yvette, France

Mathematics, 2020, vol. 8, issue 7, 1-19

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.

Keywords: cyclic projections; nonconvex sets; uniformly convex sets; strong convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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