NETT
swMATH ID:  41773 
Software Authors:  Housen Li, Johannes Schwab, Stephan Antholzer, Markus Haltmeier 
Description:  NETT: Solving Inverse Problems with Deep Neural Networks. Recovering a function or highdimensional parameter vector from indirect measurements is a central task in various scientific areas. Several methods for solving such inverse problems are well developed and well understood. Recently, novel algorithms using deep learning and neural networks for inverse problems appeared. While still in their infancy, these techniques show astonishing performance for applications like lowdose CT or various sparse data problems. However, there are few theoretical results for deep learning in inverse problems. In this paper, we establish a complete convergence analysis for the proposed NETT (Network Tikhonov) approach to inverse problems. NETT considers data consistent solutions having small value of a regularizer defined by a trained neural network. We derive wellposedness results and quantitative error estimates, and propose a possible strategy for training the regularizer. Our theoretical results and framework are different from any previous work using neural networks for solving inverse problems. A possible data driven regularizer is proposed. Numerical results are presented for a tomographic sparse data problem, which demonstrate good performance of NETT even for unknowns of different type from the training data. To derive the convergence and convergence rates results we introduce a new framework based on the absolute Bregman distance generalizing the standard Bregman distance from the convex to the nonconvex case. 
Homepage:  https://arxiv.org/abs/1803.00092 
Related Software:  DeepAdverserialRegulariser; UNet; Adam; PDENet; Wasserstein GAN; TensorFlow; DnCNN; PULSE; LoDoPaBCT; convex_learning; GitHub; BSDS; DGM; UNLocBoX; StyleGAN; BigGAN; RRR; MNIST; OPAL; BADMM 
Cited in:  19 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

NETT: solving inverse problems with deep neural networks. Zbl 1456.65038 Li, Housen; Schwab, Johannes; Antholzer, Stephan; Haltmeier, Markus 
2020

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Cited by 49 Authors
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Cited in 9 Serials
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