An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how well-posedness and convergent regularization arises within the convex-nonconvex (CNC) framework for inverse problems. We introduce a novel input weakly convex neural network (IWCNN) construction to adapt the method of learned adversarial regularization to the CNC framework. Empirically we show that our method overcomes numerical issues of previous adversarial methods.

翻译：一种解决逆问题的新兴范式是利用深度学习从数据中学习正则化器。这能带来高质量的结果，但往往以牺牲可证明的保证为代价。在本文中，我们展示了在解决逆问题的凸非凸（CNC）框架中如何实现良适性与收敛正则化。我们提出了一种新的输入弱凸神经网络（IWCNN）结构，将学习到的对抗正则化方法适配到CNC框架中。实验证明，我们的方法克服了先前对抗性方法的数值问题。