Provably Convergent Data-Driven Convex-Nonconvex Regularization
This work addresses the challenge of ensuring convergence and well-posedness in learned regularization for inverse problems, which is incremental but important for reliability in applications like imaging.
The paper tackles the lack of provable guarantees in data-driven regularization for inverse problems by introducing a convex-nonconvex framework with a novel input weakly convex neural network, achieving improved numerical stability over previous adversarial methods.
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.