Projection Methods for Uniformly Convex Expandable Sets

Stéphane Chrétien (1) , Pascal Bondon (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 L2S - Laboratoire des signaux et systèmes

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.

Mots clés: cyclic projections; nonconvex sets; uniformly convex sets; strong convergence

Domaines: Mathématiques [math]

Stéphane Chrétien, Pascal Bondon. Projection Methods for Uniformly Convex Expandable Sets. Mathematics , 2020, ⟨10.3390/math8071108⟩. ⟨hal-02896463⟩