Deep neural networks can stably solve high-dimensional, noisy, non-linear inverse problems

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

We study the problem of reconstructing solutions of inverse problems when only noisy measurements are available. We assume that the problem can be modeled with an infinite-dimensional forward operator that is not continuously invertible. Then, we restrict this forward operator to finite-dimensional spaces so that the inverse is Lipschitz continuous. For the inverse operator, we demonstrate that there exists a neural network which is a robust-to-noise approximation of the operator. In addition, we show that these neural networks can be learned from appropriately perturbed training data. We demonstrate the admissibility of this approach to a wide range of inverse problems of practical interest. Numerical examples are given that support the theoretical findings.
OriginalspracheEnglisch
Seiten (von - bis)49-91
Seitenumfang43
FachzeitschriftAnalysis and Applications
Jahrgang21
Ausgabenummer1
DOIs
PublikationsstatusVeröffentlicht - 1 Jan. 2023

ÖFOS 2012

  • 102018 Künstliche Neuronale Netze

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