Open Access
Regularization Of Inverse Problems
TLDR
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Citations
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Journal ArticleDOI
Quantitative susceptibility mapping (QSM): Decoding MRI data for a tissue magnetic biomarker.
Yi Wang,Tian-Yu Liu +1 more
TL;DR: This paper attempts to summarize the basic physical concepts and essential algorithmic steps in QSM, to describe clinical and technical issues under active development, and to provide references, codes, and testing data for readers interested inQSM.
Book ChapterDOI
The Bayesian Approach to Inverse Problems
Masoumeh Dashti,Andrew M. Stuart +1 more
TL;DR: In this paper, the authors highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations, and describe measure-preserving dynamics on the underlying infinite dimensional space.
Journal ArticleDOI
Solving ill-posed inverse problems using iterative deep neural networks
Jonas Adler,Ozan Öktem +1 more
TL;DR: In this article, a partially learned approach for the solution of ill-posed inverse problems with not necessarily linear forward operators is proposed, which builds on ideas from classical regularisation theory.
Journal ArticleDOI
Stable Architectures for Deep Neural Networks
Eldad Haber,Lars Ruthotto +1 more
TL;DR: New forward propagation techniques inspired by systems of Ordinary Differential Equations (ODE) are proposed that overcome this challenge and lead to well-posed learning problems for arbitrarily deep networks.
Journal ArticleDOI
A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications
TL;DR: A framework which allows to circumvent the intricate question of Lipschitz continuity of gradients by using an elegant and easy to check convexity condition which captures the geometry of the constraints is introduced.
References
More filters
Journal ArticleDOI
Quantitative susceptibility mapping (QSM): Decoding MRI data for a tissue magnetic biomarker.
Yi Wang,Tian-Yu Liu +1 more
TL;DR: This paper attempts to summarize the basic physical concepts and essential algorithmic steps in QSM, to describe clinical and technical issues under active development, and to provide references, codes, and testing data for readers interested inQSM.
Book ChapterDOI
The Bayesian Approach to Inverse Problems
Masoumeh Dashti,Andrew M. Stuart +1 more
TL;DR: In this paper, the authors highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations, and describe measure-preserving dynamics on the underlying infinite dimensional space.
Journal ArticleDOI
Stable Architectures for Deep Neural Networks
Eldad Haber,Lars Ruthotto +1 more
TL;DR: New forward propagation techniques inspired by systems of Ordinary Differential Equations (ODE) are proposed that overcome this challenge and lead to well-posed learning problems for arbitrarily deep networks.
Journal ArticleDOI
A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications
TL;DR: A framework which allows to circumvent the intricate question of Lipschitz continuity of gradients by using an elegant and easy to check convexity condition which captures the geometry of the constraints is introduced.
Proceedings Article
Generalization Properties of Learning with Random Features
Alessandro Rudi,Lorenzo Rosasco +1 more
TL;DR: The results shed light on the statistical computational trade-offs in large scale kernelized learning, showing the potential effectiveness of random features in reducing the computational complexity while keeping optimal generalization properties.