Provably Convergent Data-Driven Convex-Nonconvex Regularization

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-no...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-11
Main Authors: Shumaylov, Zakhar, Budd, Jeremy, Mukherjee, Subhadip, Schönlieb, Carola-Bibiane
Format: Article
Language:English
Subjects:
Convergence
Inverse problems
Neural networks
Regularization
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422