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Bayesian view on the training of invertible residual networks for solving linear inverse problems

Published version
Peer-reviewed

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Abstract

jats:titleAbstract</jats:title> jats:pLearning-based methods for inverse problems, adapting to the data’s inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works address the issue of theoretical guarantees. Recently, Arndt jats:italicet al</jats:italic> (2023 jats:italicInverse Problems</jats:italic> jats:bold39</jats:bold> 125018) exploited invertible residual networks (iResNets) to learn provably convergent regularizations given reasonable assumptions. They enforced these guarantees by approximating the linear forward operator with an iResNet. Supervised training on relevant samples introduces data dependency into the approach. An open question in this context is to which extent the data’s inherent structure influences the training outcome, i.e. the learned reconstruction scheme. Here, we address this delicate interplay of training design and data dependency from a Bayesian perspective and shed light on opportunities and limitations. We resolve these limitations by analyzing reconstruction-based training of the inverses of iResNets, where we show that this optimization strategy introduces a level of data-dependency that cannot be achieved by approximation training. We further provide and discuss a series of numerical experiments underpinning and extending the theoretical findings.</jats:p>

Description

Keywords

4901 Applied Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences

Journal Title

Inverse Problems

Conference Name

Journal ISSN

0266-5611
1361-6420

Volume Title

40

Publisher

IOP Publishing
Sponsorship
Deutsche Forschungsgemeinschaft (281474342/GRK2224/2)
Bundesministerium für Bildung und Forschung (05M20LBB)