Matthias J. Ehrhardt
About Me
I am a research associate in Dr Carola-Bibiane Schönlieb's group Cambridge Image Analysis at the Department for Applied Mathematics and Theoretical Physics, University of Cambridge.

Previously I have been working as a research associate at the Centre for Inverse Problems and the Centre for Medical Image at the University College London (UCL). In 2015, I completed my PhD in medical imaging under the supervision of Professor Simon Arridge and Dr Kris Thielemans.

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.
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

© 2014-2016 Matthias J. Ehrhardt - - last updated: December 8, 2016