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Optimal approximation of piecewise smooth functions using deep ReLU neural networks

Neural networks, 2018-12, Vol.108, p.296-330

2018

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Equivalence of approximation by convolutional neural networks and fully-connected networks

Proceedings of the American Mathematical Society, 2020-04, Vol.148 (4), p.1567-1581

2020

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A Theoretical Analysis of Deep Neural Networks and Parametric PDEs

Constructive approximation, 2022-02, Vol.55 (1), p.73-125

2022

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Extraction of Digital Wavefront Sets Using Applied Harmonic Analysis and Deep Neural Networks

SIAM journal on imaging sciences, 2019-01, Vol.12 (4), p.1936-1966

2019

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VC dimensions of group convolutional neural networks

Neural networks, 2024-01, Vol.169, p.462-474

2024

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Classification of edges using compactly supported shearlets

Applied and computational harmonic analysis, 2017-03, Vol.42 (2), p.245-293

2017

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Compressed Sensing and Its Applications: Third International MATHEON Conference 2017

1st ed. 2019., 2019

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Shearlet approximation of functions with discontinuous derivatives

Journal of approximation theory, 2016-07, Vol.207, p.127-138

Petersen, Philipp

2016

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Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs

Advances in computational mathematics, 2021-02, Vol.47 (1), Article 11

2021

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Neural network approximation and estimation of classifiers with classification boundary in a Barron class

The Annals of applied probability, 2023-08, Vol.33 (4), p.3039

2023

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Topological Properties of the Set of Functions Generated by Neural Networks of Fixed Size

Foundations of computational mathematics, 2021-04, Vol.21 (2), p.375-444

2021

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Γ-convergence of a shearlet-based Ginzburg–Landau energy

Applied and computational harmonic analysis, 2020-11, Vol.49 (3), p.727-770

2020

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Approximation properties of hybrid shearlet-wavelet frames for Sobolev spaces

Advances in computational mathematics, 2019-06, Vol.45 (3), p.1581-1606

2019

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Accuracy Analysis of a Novel Electromagnetic Navigation Procedure Versus a Standard Fluoroscopic Method for Retrograde Drilling of Osteochondritis Dissecans Lesions of the Knee

The American journal of sports medicine, 2012-04, Vol.40 (4), p.920-926

2012

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Linear independence of compactly supported separable shearlet systems

Journal of mathematical analysis and applications, 2015-08, Vol.428 (1), p.238-257

2015

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Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks

Journal of scientific computing, 2021-07, Vol.88 (1), p.22, Article 22

2021

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T2 relaxation times of the anterolateral femoral cartilage in patients after ACL-reconstruction with and without a deep lateral femoral notch sign

European journal of radiology, 2018-09, Vol.106, p.85-91

2018

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Bendlets: A second-order shearlet transform with bent elements

Applied and computational harmonic analysis, 2019-03, Vol.46 (2), p.384-399

2019

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Limitations of neural network training due to numerical instability of backpropagation

Advances in computational mathematics, 2024-02, Vol.50 (1)

2024

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WITHDRAWN: Bendlets: A second-order shearlet transform with bent elements

Applied and computational harmonic analysis, 2017-04

2017

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Deep microlocal reconstruction for limited-angle tomography

Applied and computational harmonic analysis, 2022-07, Vol.59, p.155-197

2022

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Anisotropic multiscale systems on bounded domains

Advances in computational mathematics, 2020-04, Vol.46 (2), Article 39

2020

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Retrograde Drilling of Talar Osteochondritis Dissecans Lesions: A Feasibility and Accuracy Analysis of a Novel Electromagnetic Navigation Method Versus a Standard Fluoroscopic Method

Arthroscopy, 2012-10, Vol.28 (10), p.1547-1554

2012

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The fate of osteochondral grafts after autologous osteochondral transplantation: a one-year follow-up study in a minipig model

Archives of orthopaedic and trauma surgery, 2008-11, Vol.128 (11), p.1255-1263

2008

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Shearlets on Bounded Domains and Analysis of Singularities Using Compactly Supported Shearlets

Petersen, Philipp Christian

2016

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Optimal approximation of piecewise smooth functions using deep ReLU neural networks

Equivalence of approximation by convolutional neural networks and fully-connected networks

A Theoretical Analysis of Deep Neural Networks and Parametric PDEs

Extraction of Digital Wavefront Sets Using Applied Harmonic Analysis and Deep Neural Networks

VC dimensions of group convolutional neural networks

Classification of edges using compactly supported shearlets

Compressed Sensing and Its Applications: Third International MATHEON Conference 2017

Shearlet approximation of functions with discontinuous derivatives

Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs

Neural network approximation and estimation of classifiers with classification boundary in a Barron class

Topological Properties of the Set of Functions Generated by Neural Networks of Fixed Size

Γ-convergence of a shearlet-based Ginzburg–Landau energy

Approximation properties of hybrid shearlet-wavelet frames for Sobolev spaces

Accuracy Analysis of a Novel Electromagnetic Navigation Procedure Versus a Standard Fluoroscopic Method for Retrograde Drilling of Osteochondritis Dissecans Lesions of the Knee

Linear independence of compactly supported separable shearlet systems

Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks

T2 relaxation times of the anterolateral femoral cartilage in patients after ACL-reconstruction with and without a deep lateral femoral notch sign

Bendlets: A second-order shearlet transform with bent elements

Limitations of neural network training due to numerical instability of backpropagation

WITHDRAWN: Bendlets: A second-order shearlet transform with bent elements

Deep microlocal reconstruction for limited-angle tomography

Anisotropic multiscale systems on bounded domains

Retrograde Drilling of Talar Osteochondritis Dissecans Lesions: A Feasibility and Accuracy Analysis of a Novel Electromagnetic Navigation Method Versus a Standard Fluoroscopic Method

The fate of osteochondral grafts after autologous osteochondral transplantation: a one-year follow-up study in a minipig model

Shearlets on Bounded Domains and Analysis of Singularities Using Compactly Supported Shearlets

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