106 citations · 229 across the 18 of their papers we have counts for
27 papers
Primal-dual methods and acceleration for Morozov and equality constrained regularization
Diana-Elena Mirciu, Martin Benning, Elena Resmerita
This work develops a regularization analysis of non-accelerated and accelerated primal-dual methods for solving linear inverse problems in the presence of noisy data. We investigat…
A Lifted Bregman Formulation for the Inversion of Deep Neural Networks
Xiaoyu Wang, Martin Benning
We propose a novel framework for the regularised inversion of deep neural networks. The framework is based on the authors' recent work on training feed-forward neural networks with…
Trust your source: quantifying source condition elements for variational regularisation methods
Martin Benning, Tatiana A. Bubba, Luca Ratti +1
Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide…
Convergent Data-driven Regularizations for CT Reconstruction
Samira Kabri, Alexander Auras, Danilo Riccio +4
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 computerize…
Lifted Bregman Training of Neural Networks
Xiaoyu Wang, Martin Benning
We introduce a novel mathematical formulation for the training of feed-forward neural networks with (potentially non-smooth) proximal maps as activation functions. This formulation…
Regularization of Inverse Problems: Deep Equilibrium Models versus Bilevel Learning
Danilo Riccio, Matthias J. Ehrhardt, Martin Benning
Variational regularization methods are commonly used to approximate solutions of inverse problems. In recent years, model-based variational regularization methods have often been r…
Timbre Transfer with Variational Auto Encoding and Cycle-Consistent Adversarial Networks
Russell Sammut Bonnici, Charalampos Saitis, Martin Benning
This research project investigates the application of deep learning to timbre transfer, where the timbre of a source audio can be converted to the timbre of a target audio with min…
Generalised Perceptron Learning
Xiaoyu Wang, Martin Benning
We present a generalisation of Rosenblatt's traditional perceptron learning algorithm to the class of proximal activation functions and demonstrate how this generalisation can be i…
Scanning electron diffraction tomography of strain
Robert Tovey, Duncan N. Johnstone, Sean M. Collins +4
Strain engineering is used to obtain desirable materials properties in a range of modern technologies. Direct nanoscale measurement of the three-dimensional strain tensor field wit…
Joint phase reconstruction and magnitude segmentation from velocity-encoded MRI data
Veronica Corona, Martin Benning, Lynn F. Gladden +3
Velocity-encoded MRI is an imaging technique used in different areas to assess flow motion. Some applications include medical imaging such as cardiovascular blood flow studies, and…
Bregman Itoh--Abe methods for sparse optimisation
Martin Benning, Erlend S. Riis, Carola-Bibiane Schönlieb
In this paper we propose optimisation methods for variational regularisation problems based on discretising the inverse scale space flow with discrete gradient methods. Inverse sca…
An entropic Landweber method for linear ill-posed problems
Martin Burger, Elena Resmerita, Martin Benning
The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for…
Learning the Sampling Pattern for MRI
Ferdia Sherry, Martin Benning, Juan Carlos De los Reyes +5
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 int…
Deep learning as optimal control problems: models and numerical methods
Martin Benning, Elena Celledoni, Matthias J. Ehrhardt +2
We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem…
Enhancing joint reconstruction and segmentation with non-convex Bregman iteration
Veronica Corona, Martin Benning, Matthias J. Ehrhardt +6
All imaging modalities such as computed tomography (CT), emission tomography and magnetic resonance imaging (MRI) require a reconstruction approach to produce an image. A common im…
Directional Sinogram Inpainting for Limited Angle Tomography
Robert Tovey, Martin Benning, Christoph Brune +5
In this paper we propose a new joint model for the reconstruction of tomography data under limited angle sampling regimes. In many applications of Tomography, e.g. Electron Microsc…
Modern Regularization Methods for Inverse Problems
Martin Benning, Martin Burger
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feas…
Choose your path wisely: gradient descent in a Bregman distance framework
Martin Benning, Marta M. Betcke, Matthias J. Ehrhardt +1
We propose an extension of a special form of gradient descent -- in the literature known as linearised Bregman iteration -- to a larger class of non-convex functions. We replace th…
Learning Filter Functions in Regularisers by Minimising Quotients
Martin Benning, Guy Gilboa, Joana Sarah Grah +1
Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learn…
Nonlinear Spectral Image Fusion
Martin Benning, Michael Möller, Raz Z. Nossek +4
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 mo…
Inverse Scale Space Decomposition
Marie Foged Schmidt, Martin Benning, Carola-Bibiane Schönlieb
We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on co…
Gradient descent in a generalised Bregman distance framework
Martin Benning, Marta M. Betcke, Matthias J. Ehrhardt +1
We discuss a special form of gradient descent that in the literature has become known as the so-called linearised Bregman iteration. The idea is to replace the classical (squared)…
Explorations on anisotropic regularisation of dynamic inverse problems by bilevel optimisation
Martin Benning, Carola-Bibiane Schönlieb, Tuomo Valkonen +1
We explore anisotropic regularisation methods in the spirit of [Holler & Kunisch, 14]. Based on ground truth data, we propose a bilevel optimisation strategy to compute the optimal…
Preconditioned ADMM with nonlinear operator constraint
Martin Benning, Florian Knoll, Carola-Bibiane Schönlieb +1
We are presenting a modification of the well-known Alternating Direction Method of Multipliers (ADMM) algorithm with additional preconditioning that aims at solving convex optimisa…