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.

中文翻译：

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一致凸可展开集的投影方法

医学图像重建和机器学习中的许多问题可以表述为非凸集理论可行性问题。在可以付诸实践的有效方法中，在凸约束集的情况下，连续投影算法引起了很多关注。在目前的工作中，我们提供了一种在约束集为非凸且满足某些其他结构特性的情况下的通用投影方法的理论研究。我们将我们的算法应用于磁共振成像（MRI）中的图像恢复，并根据Cadzow方法的精神将其应用于信号降噪。