Search Results for author:
Found 28 papers, 7 papers with code
Learned Regularization for Inverse Problems: Insights from a Spectral Model
The aim of this paper is to provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems.
Learning a Sparse Representation of Barron Functions with the Inverse Scale Space Flow
This paper presents a method for finding a sparse representation of Barron functions.
Resolution-Invariant Image Classification based on Fourier Neural Operators
In this paper we investigate the use of Fourier Neural Operators (FNOs) for image classification in comparison to standard Convolutional Neural Networks (CNNs).
Convergent Data-driven Regularizations for CT Reconstruction
The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT).
Analysis of Kinetic Models for Label Switching and Stochastic Gradient Descent
In this paper we provide a novel approach to the analysis of kinetic models for label switching, which are used for particle systems that can randomly switch between gradient flows in different energy landscapes.
Variational Regularization in Inverse Problems and Machine Learning
In particular we will discuss a reinterpretation of machine learning problems in the framework of regularization theory and a reinterpretation of variational methods for inverse problems in the framework of risk minimization.
Learning convex regularizers satisfying the variational source condition for inverse problems
Variational regularization has remained one of the most successful approaches for reconstruction in imaging inverse problems for several decades.
Region-of-Interest Prioritised Sampling for Constrained Autonomous Exploration Systems
In this work we present an algorithm, called the RoI Prioritised Sampling (RPS), that prioritises Region-of-Interests (RoIs) in an exploration scenario in order to utilise the limited resources of the imaging instrument on the rover effectively.
A Diffuse Interface Model for Cell Blebbing Including Membrane-Cortex Coupling with Linker Dynamics
The aim of this paper is to develop suitable models for the phenomenon of cell blebbing, which allow for computational predictions of mechanical effects including the crucial interaction of the cell membrane and the actin cortex.
Neural Architecture Search via Bregman Iterations
We propose a novel strategy for Neural Architecture Search (NAS) based on Bregman iterations.
A Bregman Learning Framework for Sparse Neural Networks
In contrast to established methods for sparse training the proposed family of algorithms constitutes a regrowth strategy for neural networks that is solely optimization-based without additional heuristics.
Ranked #164 on
Image Classification
on CIFAR-10
Identifying Untrustworthy Predictions in Neural Networks by Geometric Gradient Analysis
The susceptibility of deep neural networks to untrustworthy predictions, including out-of-distribution (OOD) data and adversarial examples, still prevent their widespread use in safety-critical applications.
Convex regularization in statistical inverse learning problems
We consider a statistical inverse learning problem, where the task is to estimate a function $f$ based on noisy point evaluations of $Af$, where $A$ is a linear operator.
Dynamically Sampled Nonlocal Gradients for Stronger Adversarial Attacks
We empirically show that by incorporating this nonlocal gradient information, we are able to give a more accurate estimation of the global descent direction on noisy and non-convex loss surfaces.
Learning Spectral Regularizations for Linear Inverse Problems
One of the main challenges in linear inverse problems is that a majority of such problems are ill-posed in the sense that the solution does not depend on the data continuously.
Variational regularisation for inverse problems with imperfect forward operators and general noise models
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.
Numerical Analysis Numerical Analysis Optimization and Control 47A52, 65J20, 65J22, 65K10
Total Variation Regularisation with Spatially Variable Lipschitz Constraints
We introduce a first order Total Variation type regulariser that decomposes a function into a part with a given Lipschitz constant (which is also allowed to vary spatially) and a jump part.
Numerical Analysis Numerical Analysis 65J20, 65J22, 68U10, 94A08
A total variation based regularizer promoting piecewise-Lipschitz reconstructions
We introduce a new regularizer in the total variation family that promotes reconstructions with a given Lipschitz constant (which can also vary spatially).
Variational Graph Methods for Efficient Point Cloud Sparsification
In this paper we propose a variational method defined on finite weighted graphs, which allows to sparsify a given 3D point cloud while giving the flexibility to control the appearance of the resulting approximation based on the chosen regularization functional.
Numerical Analysis Discrete Mathematics Data Structures and Algorithms Optimization and Control
Computing Nonlinear Eigenfunctions via Gradient Flow Extinction
In this work we investigate the computation of nonlinear eigenfunctions via the extinction profiles of gradient flows.
Adaptive Regularization of Some Inverse Problems in Image Analysis
We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems.
Nonlinear Spectral Image Fusion
In this paper we demonstrate that the framework of nonlinear spectral decompositions based on total variation (TV) regularization is very well suited for image fusion as well as more general image manipulation tasks.
Block Compressive Sensing of Image and Video with Nonlocal Lagrangian Multiplier and Patch-based Sparse Representation
Although block compressive sensing (BCS) makes it tractable to sense large-sized images and video, its recovery performance has yet to be significantly improved because its recovered images or video usually suffer from blurred edges, loss of details, and high-frequency oscillatory artifacts, especially at a low subrate.
Adaptive Regularization in Convex Composite Optimization for Variational Imaging Problems
The desired properties, robustness and effectiveness, of the regularization parameter selection in a variational framework for imaging problems are achieved by merely replacing the static regularization parameter with our adaptive one.
A Variational Model for Joint Motion Estimation and Image Reconstruction
The aim of this paper is to derive and analyze a variational model for the joint estimation of motion and reconstruction of image sequences, which is based on a time-continuous Eulerian motion model.
On Optical Flow Models for Variational Motion Estimation
The aim of this paper is to discuss and evaluate total variation based regularization methods for motion estimation, with particular focus on optical flow models.
Nonlinear Spectral Analysis via One-homogeneous Functionals - Overview and Future Prospects
We present in this paper the motivation and theory of nonlinear spectral representations, based on convex regularizing functionals.
First order algorithms in variational image processing
Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and optical flow estimation.
