Discretization of Learned NETT Regularization for Solving Inverse Problems

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 trai...

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Autores principales:	Stephan Antholzer, Markus Haltmeier
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	deep learning inverse problems discretization of NETT regularization convergence analysis learned regularizer Photography TR1-1050 Computer applications to medicine. Medical informatics R858-859.7 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/1eee8aedbed74d978d81e41441e9cb51
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id	oai:doaj.org-article:1eee8aedbed74d978d81e41441e9cb51
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spelling	oai:doaj.org-article:1eee8aedbed74d978d81e41441e9cb512021-11-25T18:03:31ZDiscretization of Learned NETT Regularization for Solving Inverse Problems10.3390/jimaging71102392313-433Xhttps://doaj.org/article/1eee8aedbed74d978d81e41441e9cb512021-11-01T00:00:00Zhttps://www.mdpi.com/2313-433X/7/11/239https://doaj.org/toc/2313-433XDeep 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.Stephan AntholzerMarkus HaltmeierMDPI AGarticledeep learninginverse problemsdiscretization of NETTregularizationconvergence analysislearned regularizerPhotographyTR1-1050Computer applications to medicine. Medical informaticsR858-859.7Electronic computers. Computer scienceQA75.5-76.95ENJournal of Imaging, Vol 7, Iss 239, p 239 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	deep learning inverse problems discretization of NETT regularization convergence analysis learned regularizer Photography TR1-1050 Computer applications to medicine. Medical informatics R858-859.7 Electronic computers. Computer science QA75.5-76.95
spellingShingle	deep learning inverse problems discretization of NETT regularization convergence analysis learned regularizer Photography TR1-1050 Computer applications to medicine. Medical informatics R858-859.7 Electronic computers. Computer science QA75.5-76.95 Stephan Antholzer Markus Haltmeier Discretization of Learned NETT Regularization for Solving Inverse Problems
description	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.
format	article
author	Stephan Antholzer Markus Haltmeier
author_facet	Stephan Antholzer Markus Haltmeier
author_sort	Stephan Antholzer
title	Discretization of Learned NETT Regularization for Solving Inverse Problems
title_short	Discretization of Learned NETT Regularization for Solving Inverse Problems
title_full	Discretization of Learned NETT Regularization for Solving Inverse Problems
title_fullStr	Discretization of Learned NETT Regularization for Solving Inverse Problems
title_full_unstemmed	Discretization of Learned NETT Regularization for Solving Inverse Problems
title_sort	discretization of learned nett regularization for solving inverse problems
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/1eee8aedbed74d978d81e41441e9cb51
work_keys_str_mv	AT stephanantholzer discretizationoflearnednettregularizationforsolvinginverseproblems AT markushaltmeier discretizationoflearnednettregularizationforsolvinginverseproblems
_version_	1718411667310641152

Discretization of Learned NETT Regularization for Solving Inverse Problems

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