106 citations · 229 across the 18 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
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…
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…
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)…