  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.
