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Augmented NETT regularization of inverse problems

Published version
Peer-reviewed

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Authors

Schwab, Johannes 
Haltmeier, Markus 

Abstract

Abstract: We propose aNETT (augmented NETwork Tikhonov) regularization as a novel data-driven reconstruction framework for solving inverse problems. An encoder-decoder type network defines a regularizer consisting of a penalty term that enforces regularity in the encoder domain, augmented by a penalty that penalizes the distance to the signal manifold. We present a rigorous convergence analysis including stability estimates and convergence rates. For that purpose, we prove the coercivity of the regularizer used without requiring explicit coercivity assumptions for the networks involved. We propose a possible realization together with a network architecture and a modular training strategy. Applications to sparse-view and low-dose CT show that aNETT achieves results comparable to state-of-the-art deep-learning-based reconstruction methods. Unlike learned iterative methods, aNETT does not require repeated application of the forward and adjoint models during training, which enables the use of aNETT for inverse problems with numerically expensive forward models. Furthermore, we show that aNETT trained on coarsely sampled data can leverage an increased sampling rate without the need for retraining.

Description

Keywords

Paper, inverse problems, learned regularizer, computed tomography, neural networks, regularization

Journal Title

Journal of Physics Communications

Conference Name

Journal ISSN

2399-6528

Volume Title

5

Publisher

IOP Publishing
Sponsorship
Division of Mathematical Sciences (DMS 1212125, DMS 1616904)
Austrian Science Fund (P 30747-N32)