21 citations · 75 across the 16 of their papers we have counts for
19 papers
Graph Residual Conjugate Diffusion: SNR-Equalized Heat Flow for Graph Signals
Jinwei Li, Daniel Tenbrinck
Diffusion models generate data by reversing a forward corruption process that typically approaches a simple Gaussian prior. Recent work has extended this framework to signals suppo…
Hybrid Methods for Robust Tabular Data Imputation
Jinwei Li, Michelle Bruch, Daniel Tenbrinck
Missing data are a fundamental challenge in statistical analysis and machine learning, as the choice of imputation method substantially impacts downstream inference. In this work,…
FlowMoDL: Model-Based Deep Learning with Conjugate-Gradient Data Consistency for Highly Accelerated 4D Flow MRI Reconstruction
Tristan Gottwald, Michelle Bruch, Mubashir-Ul Hassan +6
We present FlowMoDL, an unrolled neural network for highly accelerated 4D flow MRI reconstruction that directly optimizes for both anatomical magnitude and phase-derived velocity a…
Duality Perspective on Nonlinear Eigenproblems
Jonathan Laubmann, Manuel Friedrich, Daniel Tenbrinck
We investigate nonlinear eigenproblems for a broad class of proper, closed, convex functionals in reflexive Banach spaces. We develop a dual formulation of the nonlinear eigenprobl…
On MAP estimates and source conditions for drift identification in SDEs
Daniel Tenbrinck, Nikolas Uesseler, Philipp Wacker +1
We consider the inverse problem of identifying the drift in an SDE from observations of its solution at distinct time points. We derive a corresponding MAP estimate, we p…
Hypergraph -Laplacians and Scale Spaces
Ariane Fazeny, Daniel Tenbrinck, Kseniia Lukin +1
This paper introduces gradient, adjoint, and -Laplacian definitions for oriented hypergraphs as well as differential and averaging operators for unoriented hypergraphs. These de…
Resolution-Invariant Image Classification based on Fourier Neural Operators
Samira Kabri, Tim Roith, Daniel Tenbrinck +1
In this paper we investigate the use of Fourier Neural Operators (FNOs) for image classification in comparison to standard Convolutional Neural Networks (CNNs). Neural operators ar…
First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
Ronny Bergmann, Roland Herzog, Julián Ortiz López +1
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the cod…
Neural Architecture Search via Bregman Iterations
Leon Bungert, Tim Roith, Daniel Tenbrinck +1
We propose a novel strategy for Neural Architecture Search (NAS) based on Bregman iterations. Starting from a sparse neural network our gradient-based one-shot algorithm gradually…
A Bregman Learning Framework for Sparse Neural Networks
Leon Bungert, Tim Roith, Daniel Tenbrinck +1
We propose a learning framework based on stochastic Bregman iterations, also known as mirror descent, to train sparse neural networks with an inverse scale space approach. We deriv…
CLIP: Cheap Lipschitz Training of Neural Networks
Leon Bungert, René Raab, Tim Roith +2
Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability. For instance, DNNs are vulne…
Identifying Untrustworthy Predictions in Neural Networks by Geometric Gradient Analysis
Leo Schwinn, An Nguyen, René Raab +5
The susceptibility of deep neural networks to untrustworthy predictions, including out-of-distribution (OOD) data and adversarial examples, still prevent their widespread use in sa…
Dynamically Sampled Nonlocal Gradients for Stronger Adversarial Attacks
Leo Schwinn, An Nguyen, René Raab +4
The vulnerability of deep neural networks to small and even imperceptible perturbations has become a central topic in deep learning research. Although several sophisticated defense…
The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme
Farid Bozorgnia, Leon Bungert, Daniel Tenbrinck
In this work, we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for numerical approximation of eigen…
Fenchel Duality Theory and A Primal-Dual Algorithm on Riemannian Manifolds
Ronny Bergmann, Roland Herzog, Maurício Silva Louzeiro +2
This paper introduces a new notion of a Fenchel conjugate, which generalizes the classical Fenchel conjugation to functions defined on Riemannian manifolds. We investigate its prop…
Variational Graph Methods for Efficient Point Cloud Sparsification
Daniel Tenbrinck, Fjedor Gaede, Martin Burger
In recent years new application areas have emerged in which one aims to capture the geometry of objects by means of three-dimensional point clouds. Often the obtained data consist…
Computing Nonlinear Eigenfunctions via Gradient Flow Extinction
Leon Bungert, Martin Burger, Daniel Tenbrinck
In this work we investigate the computation of nonlinear eigenfunctions via the extinction profiles of gradient flows. We analyze a scheme that recursively subtracts such eigenfunc…
Nonlocal Inpainting of Manifold-valued Data on Finite Weighted Graphs
Ronny Bergmann, Daniel Tenbrinck
Recently, there has been a strong ambition to translate models and algorithms from traditional image processing to non-Euclidean domains, e.g., to manifold-valued data. While the t…
A Graph Framework for Manifold-valued Data
Ronny Bergmann, Daniel Tenbrinck
Graph-based methods have been proposed as a unified framework for discrete calculus of local and nonlocal image processing methods in the recent years. In order to translate variat…