Matthias J. Ehrhardt
About Me
I am a post-doctoral research associate in the Cambridge Image Analysis group at the Department for Applied Mathematics and Theoretical Physics, University of Cambridge. Previously I have been with the Centre for Inverse Problems and the Centre for Medical Image Computing at the University College London (UCL). I obtained my PhD from UCL in 2015 and my Diploma (Masters) from the University of Bremen, Germany in 2012.

My research is focussed on inverse problems in medical imaging, from models to algorithms; particularly concentrating on two aspects: i) joint reconstruction and ii) efficient stochastic algorithms.

The problem of joint reconstruction naturally arises in modern medical imaging. State-of-the-art PET-MRI (positron emission tomography and magnetic resonance imaging) scanners simultaneously acquire functional PET and anatomical MRI data. As function follows structure, both images are likely to show similar structures. A general aim of my research is to develop new methods that can exploit such expected correlation when these inverse problems are solved jointly.

When dealing with real world data sets, one often encounters that algorithms to compute state-of-the-art solutions (from a mathematical perspective) are not suitable for this large amount of data. The algorithms are often generic and therefore suboptimal for many specific problem classes. One problem class I am looking at are (dual) separable problems which are encountered in many applications, including PET, CT, parallel MRI. It is known that Kaczmarz-type algorithms that operate on subsets of the data work very well on those. However, these only apply to the simple problem of solving linear systems and may fail to converge. In my research, I study modern algorithms that can cope with much more difficult problems and extend them to be efficient for these kind of problems---with convergence guarantees and robustness!

My general research interests comprise inverse problems, non-smooth / (non-)convex / stochastic optimization, sparsity, and signal and image processing in particular application of these techniques to medical imaging.
07/2018 A python implementation of the Stochastic Primal-Dual Hybrid Gradient Algorithm (SPDHG), see arXiv, is now available on github.
07/2018 A new paper on Enhancing joint reconstruction and segmentation with non-convex Bregman iteration is out.
05/2018 New preprint available on A geometric integration approach to smooth optimisation: Foundations of the discrete gradient method.
04/2018 The Stochastic Primal-Dual Hybrid Gradient Algorithm (SPDHG) which was first proposed and analysed in arXiv is now available as part of ODL on github [link].
03/2018 Our paper Blind image fusion for hyperspectral imaging with the directional total variation has been accepted for publication in Inverse Problems.
12/2017 Our paper on Fast Quasi-Newton Algorithms for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning has been accepted for publication in IEEE Transactions on Medical Imaging.
12/2017 The software that accompanies our arxiv preprint Blind Image Fusion for Hyperspectral Imaging with the Directional Total Variation is now available on github and gitcam.
12/2017 New paper Choose Your Path Wisely: Gradient Descent in a Bregman Distance Framework is now available.
11/2017 Our paper on NiftyPET: A High-Throughput Software Platform for High Quantitative Accuracy and Precision PET Imaging and Analysis has been accepted for publication in the journal of Neuroinformatics.
10/2017 New paper out on Blind Image Fusion for Hyperspectral Imaging with the Directional Total Variation.
08/2017 A new preprint on Faster PET Reconstruction with a Stochastic Primal-Dual Hybrid Gradient Method is available. I presented it today at SPIE Optics+Photonics: Wavelets and Sparsity XVII in San Diego, USA. The official conference proceedings paper is available here.
06/2017 New paper out on Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Application available on arXiv. This is joint work with Antonin Chambolle, Peter Richtárik and Carola-Bibiane Schönlieb.
06/2017 I will be giving a lecture course on Inverse Problems with Lukas Lang in spring 2018 as part of the Mathematical Tripos at the University of Cambridge.
12/2016 Our preprint on Gradient descent in a generalised Bregman distance framework is available on arXiv.
12/2016 Call for papers for the special issue in Inverse Problems on Joint Reconstruction and Multi-Modality/Multi-Spectral Imaging, guest editors: Simon Arridge, Martin Burger and myself.
10/2016 I am giving a lecture course on Inverse Problems in Imaging which is a Part III course of the Mathematical Tripos at the University of Cambridge.
10/2016 I have joined Jesus College, Cambridge as a senior member (College Post Doctoral Associate).
06/2016 On my way to Oxford where we organize a session at the European Summer School in Modelling, Analysis and Simulation Crime and Image Processing on Inverse Problems in Imaging.
Matthias J. Ehrhardt

Cambridge Image Analysis
Department for Applied Mathematics and Theoretical Physics
University of Cambridge

Pavillion G 2.06, Centre for Mathematical Sciences, Wilberforce Road
Cambridge CB3 0WA, United Kingdom

© 2014-2018 Matthias J. Ehrhardt - - last updated: 18/12/2017