Search Results for author: Matthias J. Ehrhardt

Found 19 papers, 11 papers with code

An adaptively inexact first-order method for bilevel optimization with application to hyperparameter learning

no code implementations19 Aug 2023 Mohammad Sadegh Salehi, Subhadip Mukherjee, Lindon Roberts, Matthias J. Ehrhardt

In this work, we propose an algorithm with backtracking line search that only relies on inexact function evaluations and hypergradients and show convergence to a stationary point.

Bilevel Optimization Denoising

Designing Stable Neural Networks using Convex Analysis and ODEs

1 code implementation29 Jun 2023 Ferdia Sherry, Elena Celledoni, Matthias J. Ehrhardt, Davide Murari, Brynjulf Owren, Carola-Bibiane Schönlieb

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-Lipschitz) operators, as long as the spectral norms of the weights are appropriately constrained.

Deblurring Image Classification +2

On Optimal Regularization Parameters via Bilevel Learning

1 code implementation28 May 2023 Matthias J. Ehrhardt, Silvia Gazzola, Sebastian J. Scott

In this work, we provide a new condition that better characterizes positivity of optimal regularization parameters than the existing theory.

Analyzing Inexact Hypergradients for Bilevel Learning

no code implementations11 Jan 2023 Matthias J. Ehrhardt, Lindon Roberts

Estimating hyperparameters has been a long-standing problem in machine learning.

Bilevel Optimization

Compressed Sensing MRI Reconstruction Regularized by VAEs with Structured Image Covariance

no code implementations26 Oct 2022 Margaret Duff, Ivor J. A. Simpson, Matthias J. Ehrhardt, Neill D. F. Campbell

The covariance can model changing uncertainty dependencies caused by structure in the image, such as edges or objects, and provides a new distance metric from the manifold of learned images.

MRI Reconstruction

Imaging with Equivariant Deep Learning

no code implementations5 Sep 2022 Dongdong Chen, Mike Davies, Matthias J. Ehrhardt, Carola-Bibiane Schönlieb, Ferdia Sherry, Julián Tachella

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry.

Image Classification Self-Supervised Learning

Regularising Inverse Problems with Generative Machine Learning Models

no code implementations22 Jul 2021 Margaret Duff, Neill D. F. Campbell, Matthias J. Ehrhardt

The success of generative regularisers depends on the quality of the generative model and so we propose a set of desired criteria to assess generative models and guide future research.

BIG-bench Machine Learning Deblurring

Equivariant neural networks for inverse problems

1 code implementation23 Feb 2021 Elena Celledoni, Matthias J. Ehrhardt, Christian Etmann, Brynjulf Owren, Carola-Bibiane Schönlieb, Ferdia Sherry

In this work, we demonstrate that group equivariant convolutional operations can naturally be incorporated into learned reconstruction methods for inverse problems that are motivated by the variational regularisation approach.

Inductive Bias

Efficient Hyperparameter Tuning with Dynamic Accuracy Derivative-Free Optimization

1 code implementation6 Nov 2020 Matthias J. Ehrhardt, Lindon Roberts

Here, we apply a recent dynamic accuracy derivative-free optimization method to hyperparameter tuning, which allows inexact evaluations of the learning problem while retaining convergence guarantees.

Multi-modality imaging with structure-promoting regularisers

1 code implementation22 Jul 2020 Matthias J. Ehrhardt

Imaging with multiple modalities or multiple channels is becoming increasingly important for our modern society.

Inexact Derivative-Free Optimization for Bilevel Learning

1 code implementation23 Jun 2020 Matthias J. Ehrhardt, Lindon Roberts

A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user.

Bilevel Optimization Denoising

Structure preserving deep learning

no code implementations5 Jun 2020 Elena Celledoni, Matthias J. Ehrhardt, Christian Etmann, Robert I McLachlan, Brynjulf Owren, Carola-Bibiane Schönlieb, Ferdia Sherry

Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks.

Robust Image Reconstruction with Misaligned Structural Information

1 code implementation1 Apr 2020 Leon Bungert, Matthias J. Ehrhardt

Multi-modality (or multi-channel) imaging is becoming increasingly important and more widely available, e. g. hyperspectral imaging in remote sensing, spectral CT in material sciences as well as multi-contrast MRI and PET-MR in medicine.

Image Reconstruction

Learning the Sampling Pattern for MRI

2 code implementations20 Jun 2019 Ferdia Sherry, Martin Benning, Juan Carlos De los Reyes, Martin J. Graves, Georg Maierhofer, Guy Williams, Carola-Bibiane Schönlieb, Matthias J. Ehrhardt

The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete".


Deep learning as optimal control problems: models and numerical methods

no code implementations11 Apr 2019 Martin Benning, Elena Celledoni, Matthias J. Ehrhardt, Brynjulf Owren, Carola-Bibiane Schönlieb

We review the first order conditions for optimality, and the conditions ensuring optimality after discretisation.

Faster PET Reconstruction with Non-Smooth Priors by Randomization and Preconditioning

1 code implementation21 Aug 2018 Matthias J. Ehrhardt, Pawel Markiewicz, Carola-Bibiane Schönlieb

Uncompressed clinical data from modern positron emission tomography (PET) scanners are very large, exceeding 350 million data points (projection bins).

Blind Image Fusion for Hyperspectral Imaging with the Directional Total Variation

2 code implementations4 Oct 2017 Leon Bungert, David A. Coomes, Matthias J. Ehrhardt, Jennifer Rasch, Rafael Reisenhofer, Carola-Bibiane Schönlieb

In this paper, we propose a method for increasing the spatial resolution of a hyperspectral image by fusing it with an image of higher spatial resolution that was obtained with a different imaging modality.

Blind Super-Resolution Super-Resolution

Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications

2 code implementations15 Jun 2017 Antonin Chambolle, Matthias J. Ehrhardt, Peter Richtárik, Carola-Bibiane Schönlieb

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable.

Multi-Contrast MRI Reconstruction with Structure-Guided Total Variation

no code implementations20 Nov 2015 Matthias J. Ehrhardt, Marta M. Betcke

Many clinical imaging studies acquire MRI data for more than one of these contrasts---such as for instance T1 and T2 weighted images---which makes the overall scanning procedure very time consuming.

Anatomy MRI Reconstruction

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