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Keywords = discretization of NETT

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13 pages, 1403 KiB  
Article
Discretization of Learned NETT Regularization for Solving Inverse Problems
by Stephan Antholzer and Markus Haltmeier
J. Imaging 2021, 7(11), 239; https://doi.org/10.3390/jimaging7110239 - 15 Nov 2021
Cited by 8 | Viewed by 1928
Abstract
Deep learning based reconstruction methods deliver outstanding results for solving inverse problems and are therefore becoming increasingly important. A recently invented class of learning-based reconstruction methods is the so-called NETT (for Network Tikhonov Regularization), which contains a trained neural network as regularizer in [...] Read more.
Deep learning based reconstruction methods deliver outstanding results for solving inverse problems and are therefore becoming increasingly important. A recently invented class of learning-based reconstruction methods is the so-called NETT (for Network Tikhonov Regularization), which contains a trained neural network as regularizer in generalized Tikhonov regularization. The existing analysis of NETT considers fixed operators and fixed regularizers and analyzes the convergence as the noise level in the data approaches zero. In this paper, we extend the frameworks and analysis considerably to reflect various practical aspects and take into account discretization of the data space, the solution space, the forward operator and the neural network defining the regularizer. We show the asymptotic convergence of the discretized NETT approach for decreasing noise levels and discretization errors. Additionally, we derive convergence rates and present numerical results for a limited data problem in photoacoustic tomography. Full article
(This article belongs to the Special Issue Inverse Problems and Imaging)
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