121 citations · 327 across the 38 of their papers we have counts for
51 papers
Taming Nonconvexity with Epigraph Lifting
Clara Lage, Hok Shing Wong, Matthias Ehrhardt
We consider inverse problems regularized by a trained neural network with \emph{convex activations} and \emph{unrestricted weights}. The resulting optimization problem is generally…
Bilevel Learning via Inexact Stochastic Gradient Descent
Mohammad Sadegh Salehi, Subhadip Mukherjee, Lindon Roberts +1
Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learni…
PET Rapid Image Reconstruction Challenge (PETRIC)
Casper da Costa-Luis, Matthias J. Ehrhardt, Christoph Kolbitsch +4
Introduction: We describe the foundation of PETRIC, an image reconstruction challenge to minimise the computational runtime of related algorithms for Positron Emission Tomography (…
Stable neural networks and connections to continuous dynamical systems
Matthias J. Ehrhardt, Davide Murari, Ferdia Sherry
The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhanci…
Learning Regularization Functionals for Inverse Problems: A Comparative Study
Johannes Hertrich, Hok Shing Wong, Alexander Denker +16
In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insig…
Fast PET Reconstruction with Variance Reduction and Prior-Aware Preconditioning
Matthias J. Ehrhardt, Zeljko Kereta, Georg Schramm
We investigate subset-based optimization methods for positron emission tomography (PET) image reconstruction incorporating a regularizing prior. PET reconstruction methods that use…
Stochastic Multiresolution Image Sketching for Inverse Imaging Problems
Alessandro Perelli, Carola-Bibiane Schonlieb, Matthias J. Ehrhardt
A challenge in high-dimensional inverse problems is developing iterative solvers to find the accurate solution of regularized optimization problems with low computational cost. An…
Complex extension of optical flow and its practical evaluation for undersampled dynamic MRI
Matthias J. Ehrhardt, Marco Mauritz
Reconstructing high-quality images from undersampled dynamic MRI data is a challenging task and important for the success of this imaging modality. To remedy the naturally occurrin…
Bilevel Learning with Inexact Stochastic Gradients
Mohammad Sadegh Salehi, Subhadip Mukherjee, Lindon Roberts +1
Bilevel learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers,…
Efficient gradient-based methods for bilevel learning via recycling Krylov subspaces
Matthias J. Ehrhardt, Silvia Gazzola, Sebastian J. Scott
Many optimization problems require hyperparameters, i.e., parameters that must be pre-specified in advance, such as regularization parameters and parametric regularizers in variati…
An Adaptively Inexact Method for Bilevel Learning Using Primal-Dual Style Differentiation
Lea Bogensperger, Matthias J. Ehrhardt, Thomas Pock +2
We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minim…
Accelerated Convergent Motion Compensated Image Reconstruction
Claire Delplancke, Kris Thielemans, Matthias J. Ehrhardt
Motion correction aims to prevent motion artefacts which may be caused by respiration, heartbeat, or head movements for example. In a preliminary step, the measured data is divided…
A primal-dual algorithm for image reconstruction with input-convex neural network regularizers
Matthias J. Ehrhardt, Subhadip Mukherjee, Hok Shing Wong
We address the optimization problem in a data-driven variational reconstruction framework, where the regularizer is parameterized by an input-convex neural network (ICNN). While gr…
A Guide to Stochastic Optimisation for Large-Scale Inverse Problems
Matthias J. Ehrhardt, Zeljko Kereta, Jingwei Liang +1
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dra…
Greedy Learning to Optimize with Convergence Guarantees
Patrick Fahy, Mohammad Golbabaee, Matthias J. Ehrhardt
Learning to optimize (L2O) is an approach that leverages training data to accelerate the solution of optimization problems. Many approaches use unrolling to parametrize the update…
Analysis of Primal-Dual Langevin Algorithms
Martin Burger, Matthias J. Ehrhardt, Lorenz Kuger +1
We analyze a recently proposed class of algorithms for the problem of sampling from probability distributions in with a Lebesgue density of the form $μ^\ast…
Practical Acceleration of the Condat-Vũ Algorithm
Derek Driggs, Matthias J. Ehrhardt, Carola-Bibiane Schönlieb +1
The Condat-Vũ algorithm is a widely used primal-dual method for optimizing composite objectives of three functions. Several algorithms for optimizing composite objectives of two fu…
An adaptively inexact first-order method for bilevel optimization with application to hyperparameter learning
Mohammad Sadegh Salehi, Subhadip Mukherjee, Lindon Roberts +1
Various tasks in data science are modeled utilizing the variational regularization approach, where manually selecting regularization parameters presents a challenge. The difficulty…
Proximal Langevin Sampling With Inexact Proximal Mapping
Matthias J. Ehrhardt, Lorenz Kuger, Carola-Bibiane Schönlieb
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribut…
Designing Stable Neural Networks using Convex Analysis and ODEs
Ferdia Sherry, Elena Celledoni, Matthias J. Ehrhardt +3
Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lip…
On Optimal Regularization Parameters via Bilevel Learning
Matthias J. Ehrhardt, Silvia Gazzola, Sebastian J. Scott
Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori…
Uncertainty Quantification in CT pulmonary angiography
Adwaye M Rambojun, Hend Komber, Jennifer Rossdale +4
Computed tomography (CT) imaging of the thorax is widely used for the detection and monitoring of pulmonary embolism (PE). However, CT images can contain artifacts due to the acqui…
Analyzing Inexact Hypergradients for Bilevel Learning
Matthias J. Ehrhardt, Lindon Roberts
Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem.…
Stochastic Primal Dual Hybrid Gradient Algorithm with Adaptive Step-Sizes
Antonin Chambolle, Claire Delplancke, Matthias J. Ehrhardt +2
In this work we propose a new primal-dual algorithm with adaptive step-sizes. The stochastic primal-dual hybrid gradient (SPDHG) algorithm with constant step-sizes has become widel…