Poster
in
Workshop: Learning-Based Solutions for Inverse Problems
Provably Convergent Data-Driven Convex-Nonconvex Regularization
Zakhar Shumaylov · Jeremy Budd · Subhadip Mukherjee · Carola-Bibiane Schönlieb
Keywords: [ convergent regularisation ] [ weak convexity ] [ Inverse Problems ] [ input-convex neural networks ] [ data-driven regularization ] [ variational imaging ]
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 regularisation 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.