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Bregman Itoh–Abe Methods for Sparse Optimisation
Abstract: In this paper we propose optimisation methods for variational regularisation problems based on discretising the inverse scale space flow with discrete gradient methods. Inverse scale space flow generalises gradient...
Focus U-Net
BACKGROUND: Colonoscopy remains the gold-standard screening for colorectal cancer. However, significant miss rates for polyps have been reported, particularly when there are multiple small adenomas. This presents an opportunity...
Bregman Itoh–Abe Methods for Sparse Optimisation
Abstract: In this paper we propose optimisation methods for variational regularisation problems based on discretising the inverse scale space flow with discrete gradient methods. Inverse scale space flow generalises gradient...
An anisotropic interaction model for simulating fingerprints.
Bertram Düring, Carsten Gottschlich, Stephan Huckemann, Lisa Maria Kreusser, Carola-Bibiane Schönlieb
Feb 18, 2019
Evidence suggests that both the interaction of so-called Merkel cells and the epidermal stress distribution play an important role in the formation of fingerprint patterns during pregnancy. To model the formation of fingerprint...
Variational regularisation for inverse problems with imperfect forward operators and general noise models.
Leon Bungert, martin.burger@fau.de, Martin Burger, Yury Korolev, Carola-Bibiane Schönlieb
Jul 28, 2021
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to...
Kullback–Leibler divergence f-divergences Wasserstein distances imperfect forward models Banach lattices Bregman distances discrepancy principle
Published by: Inverse problems
Deep learning as optimal control problems
Martin Benning, Elena Celledoni, Matthias J. Ehrhardt, Brynjulf Owren, Carola-Bibiane Schönlieb
Dec 01, 2019
We consider recent work of [18] and [9], where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We review the first...
Γ-Convergence of an Ambrosio-Tortorelli approximation scheme for image segmentation
Given an image u0, the aim of minimising the Mumford-Shah functional is to find a decomposition of the image domain into sub-domains and a piecewise smooth approximation u of u0 such that u varies smoothly within each...
Variational regularisation for inverse problems with imperfect forward operators and general noise models
Leon Bungert, martin.burger@fau.de, Martin Burger, Yury Korolev, Carola-Bibiane Schönlieb
Dec 03, 2020
Variational regularisation for inverse problems with imperfect forward operators and general noise models
Leon Bungert, martin.burger@fau.de, Martin Burger, Yury Korolev, Carola-Bibiane Schönlieb
Dec 03, 2020
A Geometric Integration Approach to Nonsmooth, Nonconvex Optimisation
The optimisation of nonsmooth, nonconvex functions without access to gradients is a particularly challenging problem that is frequently encountered, for example in model parameter optimisation problems. Bilevel optimisation...
Bilevel optimisation Clarke subdifferential Derivative-free optimisation Discrete gradient methods Geometric numerical integration Nonconvex optimisation Nonsmooth optimisation /dk/atira/pure/subjectarea/asjc/2600/2603 name=Analysis /dk/atira/pure/subjectarea/asjc/2600/2605 name=Computational Mathematics /dk/atira/pure/subjectarea/asjc/1700/1703 name=Computational Theory and Mathematics /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics
Accelerating Variance-Reduced Stochastic Gradient Methods
Variance reduction is a crucial tool for improving the slow convergence of stochastic gradient descent. Only a few variance-reduced methods, however, have yet been shown to directly benefit from Nesterov’s acceleration...
Pattern formation of a nonlocal, anisotropic interaction model
Martin Burger, Bertram Düring, Lisa Maria Kreusser, Peter A. Markowich, Carola Bibiane Schönlieb
Mar 01, 2018
We consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. An example of this class of models is the so-called...
Equivariant neural networks for inverse problems
Elena Celledoni, Matthias J. Ehrhardt, Christian Etmann, Brynjulf Owren, Carola-Bibiane Schönlieb, Ferdia Sherry
Aug 31, 2021
In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research...
equivariance Image reconstruction Neural Networks variational regularisation /dk/atira/pure/subjectarea/asjc/2600/2614 name=Theoretical Computer Science /dk/atira/pure/subjectarea/asjc/1700/1711 name=Signal Processing /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics /dk/atira/pure/subjectarea/asjc/1700/1706 name=Computer Science Applications /dk/atira/pure/subjectarea/asjc/2600/2610 name=Mathematical Physics
Accelerating Variance-Reduced Stochastic Gradient Methods
Variance reduction is a crucial tool for improving the slow convergence of stochastic gradient descent. Only a few variance-reduced methods, however, have yet been shown to directly benefit from Nesterov’s acceleration...
Iterative phase contrast CT reconstruction with novel tomographic operator and data-driven prior.
Stefano van Gogh, Subhadip Mukherjee, Jinqiu Xu, Zhentian Wang, Michał Rawlik, Zsuzsanna Varga, Rima Alaifari, Carola-Bibiane Schönlieb, Marco Stampanoni
Sep 02, 2022
Equivariant neural networks for inverse problems
Elena Celledoni, Matthias J. Ehrhardt, Christian Etmann, Brynjulf Owren, Carola-Bibiane Schönlieb, Ferdia Sherry
Aug 31, 2021
In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research...
equivariance Image reconstruction Neural Networks variational regularisation /dk/atira/pure/subjectarea/asjc/2600/2614 name=Theoretical Computer Science /dk/atira/pure/subjectarea/asjc/1700/1711 name=Signal Processing /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics /dk/atira/pure/subjectarea/asjc/1700/1706 name=Computer Science Applications /dk/atira/pure/subjectarea/asjc/2600/2610 name=Mathematical Physics
Choose your Path Wisely
We propose an extension of a special form of gradient descent --- in the literature known as linearised Bregman iteration --- to a larger class of non-convex functions. We replace the classical (squared) two norm metric in the...
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