Networks for nonlinear diffusion problems in imaging

DOI10.1007/s10851-019-00901-3zbMath1434.68496DBLPjournals/jmiv/ArridgeH20arXiv1811.12084OpenAlexW2972341443WikidataQ92000482 ScholiaQ92000482MaRDI QIDQ1988365

Andreas Hauptmann, Simon R. Arridge

Publication date: 23 April 2020

Published in: Journal of Mathematical Imaging and Vision (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.12084

zbMATH Keywords

neural networkspartial differential equationsnonlinear diffusionnonlinear inverse problemsdeep learningimage flow

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Nonlinear parabolic equations (35K55) Inverse problems for PDEs (35R30) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) PDEs in connection with computer science (35Q68)

Related Items (7)

Learning and correcting non-Gaussian model errors ⋮ On the randomised stability constant for inverse problems ⋮ Deep learning methods for partial differential equations and related parameter identification problems ⋮ Sequential Model Correction for Nonlinear Inverse Problems ⋮ Connections between numerical algorithms for PDEs and neural networks ⋮ On mathematical modeling in image reconstruction and beyond ⋮ Deep learning architectures for nonlinear operator functions and nonlinear inverse problems

Uses Software

• TensorFlow
• U-Net
• PDE-Net
• STL-10 dataset
• DGM

Cites Work

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• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
• Hidden physics models: machine learning of nonlinear partial differential equations
• DGM: a deep learning algorithm for solving partial differential equations
• Stable backward diffusion models that minimise convex energies
• PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network
• A data-driven edge-preserving D-bar method for electrical impedance tomography
• Edge-promoting reconstruction of absorption and diffusivity in optical tomography
• Hierarchical models in statistical inverse problems and the Mumford–Shah functional
• Hypermodels in the Bayesian imaging framework
• Vector-Valued Image Processing by Parallel Level Sets
• Solving ill-posed inverse problems using iterative deep neural networks
• Stable architectures for deep neural networks
• Deep Convolutional Neural Network for Inverse Problems in Imaging
• Deep Convolutional Framelets: A General Deep Learning Framework for Inverse Problems
• Deep learning for photoacoustic tomography from sparse data
• Solving parametric PDE problems with artificial neural networks
• Understanding Machine Learning

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