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Unsupervised Image Restoration Using Partially Linear Denoisers.
Deep neural network based methods are the state of the art in various image restoration problems. Standard supervised learning frameworks require a set of noisy measurement and clean image pairs for which a distance between the...
Stability analysis of line patterns of an anisotropic interaction model
Motivated by the formation of fingerprint patterns, we consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. This...
Equilibria of an anisotropic nonlocal interaction equation
In this paper, we study the equilibria of an anisotropic, nonlocal aggregation equation with nonlinear diffusion which does not possess a gradient flow structure. Here, the anisotropy is induced by an underlying tensor field....
Finite volume methods Nonlinear diffusion Nonlocal aggregation pattern formation Stationary states /dk/atira/pure/subjectarea/asjc/2600/2603 name=Analysis /dk/atira/pure/subjectarea/asjc/2600/2607 name=Discrete Mathematics and Combinatorics /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics
Equilibria of an anisotropic nonlocal interaction equation
In this paper, we study the equilibria of an anisotropic, nonlocal aggregation equation with nonlinear diffusion which does not possess a gradient flow structure. Here, the anisotropy is induced by an underlying tensor field....
Finite volume methods Nonlinear diffusion Nonlocal aggregation pattern formation Stationary states /dk/atira/pure/subjectarea/asjc/2600/2603 name=Analysis /dk/atira/pure/subjectarea/asjc/2600/2607 name=Discrete Mathematics and Combinatorics /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics
Stability analysis of line patterns of an anisotropic interaction model
Motivated by the formation of fingerprint patterns, we consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. This...
Variational Osmosis for Non-linear Image Fusion.
Simone Parisotto, Luca Calatroni, Aurelie Bugeau, Nicolas Papadakis, Carola-Bibiane Schonlieb
Apr 23, 2020
We propose a new variational model for non-linear image fusion. Our approach is based on the use of an osmosis energy term related to the one studied in Vogel et al. [44] and Weickert et al. [45]. The minimization of the...
Learning the Sampling Pattern for MRI.
Ferdia Sherry, Martin Benning, Juan Carlos De Los Reyes, Martin J Graves, Georg Maierhofer, Guy Williams, Carola-Bibiane Schonlieb, Matthias J Ehrhardt
Aug 18, 2020
The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI)...
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...
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
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...
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
Analysis of artifacts in shell-based image inpainting
In this paper we study a class of fast geometric image inpainting methods based on the idea of lling the inpainting domain in successive shells from its boundary inwards. Image pixels are lled by assigning them a color equal...
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
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...
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...
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
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...
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...
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