scholarly journals Learning regularization parameters of inverse problems via deep neural networks

2021 ◽  
Author(s):  
Babak Afkham ◽  
Julianne Chung ◽  
Matthias Chung
Keyword(s):  
Neural Networks ◽  
Inverse Problems ◽  
Deep Neural Networks ◽  
Regularization Parameters

scholarly journals Big in Japan: Regularizing Networks for Solving Inverse Problems

2019 ◽  
Vol 62 (3) ◽  
pp. 445-455
Author(s):  
Johannes Schwab ◽  
Stephan Antholzer ◽  
Markus Haltmeier
Keyword(s):  
Neural Networks ◽  
Inverse Problems ◽  
Regularization Method ◽  
Deep Neural Networks ◽  
Convergence Rates ◽  
Null Space ◽  
Space Network ◽  
Special Cases ◽  
Data Problem ◽  
Sparse Data Problem

Abstract Deep learning and (deep) neural networks are emerging tools to address inverse problems and image reconstruction tasks. Despite outstanding performance, the mathematical analysis for solving inverse problems by neural networks is mostly missing. In this paper, we introduce and rigorously analyze families of deep regularizing neural networks (RegNets) of the form $$\mathbf {B}_\alpha + \mathbf {N}_{\theta (\alpha )} \mathbf {B}_\alpha $$Bα+Nθ(α)Bα, where $$\mathbf {B}_\alpha $$Bα is a classical regularization and the network $$\mathbf {N}_{\theta (\alpha )} \mathbf {B}_\alpha $$Nθ(α)Bα is trained to recover the missing part $${\text {Id}}_X - \mathbf {B}_\alpha $$IdX-Bα not found by the classical regularization. We show that these regularizing networks yield a convergent regularization method for solving inverse problems. Additionally, we derive convergence rates (quantitative error estimates) assuming a sufficient decay of the associated distance function. We demonstrate that our results recover existing convergence and convergence rates results for filter-based regularization methods as well as the recently introduced null space network as special cases. Numerical results are presented for a tomographic sparse data problem, which clearly demonstrate that the proposed RegNets improve classical regularization as well as the null space network.

scholarly journals Deep Neural Networks for Inverse Problems with Pseudodifferential Operators: An Application to Limited-Angle Tomography

2021 ◽  
Vol 14 (2) ◽  
pp. 470-505
Author(s):  
Tatiana A. Bubba ◽  
Mathilde Galinier ◽  
Matti Lassas ◽  
Marco Prato ◽  
Luca Ratti ◽  
...  
Keyword(s):  
Neural Networks ◽  
Inverse Problems ◽  
Deep Neural Networks ◽  
Pseudodifferential Operators ◽  
Limited Angle

Using Deep Neural Networks for Inverse Problems in Imaging: Beyond Analytical Methods

2018 ◽  
Vol 35 (1) ◽  
pp. 20-36 ◽  
Author(s):  
Alice Lucas ◽  
Michael Iliadis ◽  
Rafael Molina ◽  
Aggelos K. Katsaggelos
Keyword(s):  
Neural Networks ◽  
Inverse Problems ◽  
Analytical Methods ◽  
Deep Neural Networks

scholarly journals NETT: solving inverse problems with deep neural networks

2020 ◽  
Vol 36 (6) ◽  
pp. 065005 ◽  
Author(s):  
Housen Li ◽  
Johannes Schwab ◽  
Stephan Antholzer ◽  
Markus Haltmeier
Keyword(s):  
Neural Networks ◽  
Inverse Problems ◽  
Deep Neural Networks

Deep neural networks trained with heavier data augmentation learn features closer to representations in hIT

2018 ◽  
Author(s):  
Alex Hernández-García ◽  
Johannes Mehrer ◽  
Nikolaus Kriegeskorte ◽  
Peter König ◽  
Tim C. Kietzmann
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Data Augmentation
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