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Open AccessArticle

Projection Methods for Uniformly Convex Expandable Sets

1
Laboratoire ERIC, Université Lyon 2, 69500 Bron, France
2
The Alan Turing Institute, London NW1 2DB, UK
3
Data Science Division, The National Physical Laboratory, Teddington TW11 0LW, UK
4
Laboratoire des Signaux et Systèmes, CentraleSupélec, CNRS, Université Paris-Saclay, 91190 Gif-sur-Yvette, France
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(7), 1108; https://doi.org/10.3390/math8071108
Received: 21 February 2020 / Revised: 19 June 2020 / Accepted: 22 June 2020 / Published: 6 July 2020
(This article belongs to the Special Issue New Trends in Machine Learning: Theory and Practice)
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. View Full-Text
Keywords: cyclic projections; nonconvex sets; uniformly convex sets; strong convergence cyclic projections; nonconvex sets; uniformly convex sets; strong convergence
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MDPI and ACS Style

Chrétien, S.; Bondon, P. Projection Methods for Uniformly Convex Expandable Sets. Mathematics 2020, 8, 1108. https://doi.org/10.3390/math8071108

AMA Style

Chrétien S, Bondon P. Projection Methods for Uniformly Convex Expandable Sets. Mathematics. 2020; 8(7):1108. https://doi.org/10.3390/math8071108

Chicago/Turabian Style

Chrétien, Stéphane; Bondon, Pascal. 2020. "Projection Methods for Uniformly Convex Expandable Sets" Mathematics 8, no. 7: 1108. https://doi.org/10.3390/math8071108

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