Philipp Petersen
TitleCited byYear
Optimal approximation of piecewise smooth functions using deep ReLU neural networks
P Petersen, F Voigtlaender
Neural Networks 108, 296-330, 2018
Optimal approximation with sparsely connected deep neural networks
H Bölcskei, P Grohs, G Kutyniok, P Petersen
SIAM Journal on Mathematics of Data Science 1 (1), 8-45, 2019
Classification of edges using compactly supported shearlets
G Kutyniok, P Petersen
Appl. Comput. Harmon. Anal., 0
Topological properties of the set of functions generated by neural networks of fixed size
P Petersen, M Raslan, F Voigtlaender
arXiv preprint arXiv:1806.08459, 2018
Equivalence of approximation by convolutional neural networks and fully-connected networks
P Petersen, F Voigtlaender
arXiv preprint arXiv:1809.00973, 2018
Memory-optimal neural network approximation
H Bölcskei, P Grohs, G Kutyniok, P Petersen
Wavelets and Sparsity XVII 10394, 103940Q, 2017
A theoretical analysis of deep neural networks and parametric PDEs
G Kutyniok, P Petersen, M Raslan, R Schneider
arXiv preprint arXiv:1904.00377, 2019
Deep ReLU Networks and High-Order Finite Element Methods
J Opschoor, P Petersen, C Schwab
SAM Technical Report, 2019
Error bounds for approximations with deep ReLU neural networks in norms
I Gühring, G Kutyniok, P Petersen
arXiv preprint arXiv:1902.07896, 2019
Bendlets: A second-order shearlet transform with bent elements
C Lessig, P Petersen, M Schäfer
Applied and computational Harmonic Analysis, 2017
Regularization and numerical solution of the inverse scattering problem using shearlet frames
G Kutyniok, V Mehrmann, PC Petersen
Journal of Inverse and Ill-posed Problems 25 (3), 287-309, 2017
Shearlet approximation of functions with discontinuous derivatives
P Petersen
Journal of Approximation Theory 207, 127-138, 2016
Shearlets on bounded domains and analysis of singularities using compactly supported shearlets
PC Petersen
Berlin, Technische Universität Berlin, 2016
Linear independence of compactly supported separable shearlet systems
J Ma, P Petersen
Journal of Mathematical Analysis and Applications 428 (1), 238-257, 2015
Anisotropic multiscale systems on bounded domains
P Grohs, G Kutyniok, J Ma, P Petersen, M Raslan
arXiv preprint arXiv:1510.04538, 2015
Approximation in with deep ReLU neural networks
F Voigtlaender, P Petersen
arXiv preprint arXiv:1904.04789, 2019
Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks
H Andrade-Loarca, G Kutyniok, O Öktem, P Petersen
arXiv preprint arXiv:1901.01388, 2019
Optimal approximation with sparsely connected deep neural networks
G Kutyniok, H Bölcskei, P Grohs, P Petersen
Preprint, 0
Approximation properties of shearlet frames for Sobolev spaces
P Petersen, M Raslan
arXiv preprint arXiv:1712.01047, 2017
DGD Approximation Theory Workshop
S Keiper, G Kutyniok, P Petersen
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Articles 1–20