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...

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Published in:arXiv.org 2023-11
Main Authors: Shumaylov, Zakhar, Budd, Jeremy, Mukherjee, Subhadip, Schönlieb, Carola-Bibiane
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Language:English
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Convergence
Inverse problems
Neural networks
Regularization
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Budd, Jeremy
Mukherjee, Subhadip
Schönlieb, Carola-Bibiane
description 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.
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subjects Convergence
Inverse problems
Neural networks
Regularization
title Provably Convergent Data-Driven Convex-Nonconvex Regularization
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