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：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。该方法虽能获得高质量结果，但往往以牺牲可证明性保证为代价。本研究展示了在凸-非凸（CNC）框架下如何实现逆问题的适定性与收敛性正则化。我们提出一种新型输入弱凸神经网络（IWCNN）结构，将学习型对抗正则化方法适配至CNC框架。实验表明，本方法克服了先前对抗性方法存在的数值问题。