English

Provably Convergent Data-Driven Convex-Nonconvex Regularization

Machine Learning 2023-11-06 v2 Computer Vision and Pattern Recognition Machine Learning

Abstract

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.

Keywords

Cite

@article{arxiv.2310.05812,
  title  = {Provably Convergent Data-Driven Convex-Nonconvex Regularization},
  author = {Zakhar Shumaylov and Jeremy Budd and Subhadip Mukherjee and Carola-Bibiane Schönlieb},
  journal= {arXiv preprint arXiv:2310.05812},
  year   = {2023}
}

Comments

Accepted to NeurIPS 2023 Workshop on Deep Learning and Inverse Problems

R2 v1 2026-06-28T12:44:47.836Z