About me

I am a Prize Fellow at the Institute for Mathematical Innovation, University of Bath. My research lies in the interface of optimization, inverse imaging problems and machine learning where I develop algorithms that are efficient enough for large-scale applications with proven convergence guarantees and robustness. My work bridges mathematical theory to various applications including medical imaging, biology and geophysics. My collaborators have a variety of backgrounds and include mathematicians, computer scientists, physicists, geophysicists and medical doctors.

Generally, I am interested in inverse problems, non-smooth / (non-)convex / stochastic optimization, sparsity, and signal and image processing in particular application of these techniques to medical imaging.

Short Bio: I was a post-doctoral research associate in the Cambridge Image Analysis group at the Department for Applied Mathematics and Theoretical Physics, University of Cambridge from 2016-2018. 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.

m.ehrhardt@bath.ac.uk

Office: 6 West, 1.08
Tel: 0044 1225 38 6194
University of Bath
Bath BA2 7JU
United Kingdom

News

01/2020	Congratulations to my student Margaret Duff who was invited to present her research at the UK Parliament as part of STEM for BRITAIN 2020.
01/2020	Chris Budd (Bath, UK) is turning 60 and we are celebrating this with a workshop on 4 March 2020 in Bath, see here for more details. This event is organized by Arie Iserles (Cambridge, UK), Carola-Bibiane Schönlieb (Cambridge, UK) and myself.
12/2019	New paper out on SIRF: Synergistic Image Reconstruction Framework to be published in Computer Physics Communication. This is joint work with many people from all around the work lead by Kris Thielemans (UCL, UK).
12/2019	I am organising the 2020 LMS-Bath Symposium on the Mathematics of Machine Learning together with Philip Aston (Surrey), Catherine Higham (Glasgow) and Clarice Poon (Bath).
12/2019	Our paper on Deep learning as optimal control problems: models and numerical methods got published in the Journal of Computational Dynamics. This is joint work with Martin Benning (QMUL, UK), Elena Celledoni (NTNU, Norway), Brynjulf Owren (NTNU, Norway) and Carola-Bibiane Schönlieb (Cambridge, UK).
11/2019	Congratulations to my student Sam Cortinhas who won an IMI best poster prize.
10/2019	New paper out on Accelerating Variance-Reduced Stochastic Gradient Methods. This is joint work with Derek Driggs and Carola-Bibiane Schönlieb (both Cambridge).
09/2019	Are you a motivated researcher looking for a PostDoc position in the UK? Are you interested in Machine Learning? Are you interested in Imaging? Then we want YOU! Apply here.
08/2019	Our paper on Faster PET reconstruction with non-smooth priors by randomization and preconditioning just got accepted in Physics in Medicine & Biology.
07/2019	I am looking for outstanding candidates for a 3-year PostDoc position in Inverse Problems and Optimization, see link for more information.
06/2019	Margaret Duff now starts the research part of her PhD on machine learning and imaging. She is supervised by Neill Campbell and myself.
06/2019	New paper out on Learning the Sampling Pattern for MRI. This is joint work with Ferdia Sherry, Martin J. Graves, Georg Maierhofer, Guy Williams, Carola-Bibiane Schönlieb (all Cambridge, UK), Martin Benning (Queen Mary, London, UK) and Juan Carlos De los Reyes (Quito, Ecuador).
06/2019	We were awarded a grant from the Faraday Institute for "Quantitative Imaging of Multi-Scale Dynamic Phenomena at Electrochemical Interfaces". This is a multi-institute collaboration lead by Nigel Browning, Liverpool. As part of this project a PostDoc in Bath will be advertised soon.
06/2019	Konstantin Mishchenko is visiting us from KAUST, Saudi Arabia for two weeks in June 2019.
05/2019	I was awarded a Leverhulme Early Career fellowship on "A Continuous Approach to Machine Learning for Image Reconstruction" to start in May 2020.
04/2019	I am looking for outstanding candidates for a 3-year PostDoc position on inverse problems, PET imaging and optimisation, see link for more information. This position is part of our EPSRC project EP/S026045/1 on Improving Localisation, Diagnosis and Quantification in Clinical and Medical PET Imaging with Randomised Optimisation.
04/2019	New preprint out on the connection between deep learning and optimal control with ODEs: Deep learning as optimal control problems: models and numerical methods. This is joint work with Martin Benning (QMUL, London, UK), Elena Celledoni (NTNU, Norway), Brynjulf Owren (NTNU, Norway) and Carola-Bibiane Schönlieb (Cambridge, UK).
03/2019	Our paper on Enhancing joint reconstruction and segmentation with non-convex Bregman iteration got accepted for publication in IOP Inverse Problems. This is joint work with many UK colleagues, including Veronica Corona (mathematics, Cambridge), Martin Benning (QMUL, London), Lynn Gladden (chemical engineering, Cambridge) and Carola-Bibiane Schönlieb (mathematics, Cambridge).
01/2019	In February, Eric Baruch Gutiérrez Castillo will be joining us from Mexico as a PhD student. He is jointly supervised by Melina Freitag and myself.

News archive:

2018

11/2018	Our paper on Incorporating Structural Prior Information and Sparsity into EIT using Parallel Level Sets got accepted for Inverse Problems and Imaging. This is joint work with Ville Kolehmainen (Finland) and Simon Arridge (UK).
10/2018	Evelyn Cueva from the University of Chile, Santiago, Chile is visiting us for 5 months.
10/2018	SIAM Optimization has now published our paper on Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications.
09/2018	I started my new position at the University of Bath as a Prize Fellow of the Institute for Mathematical Innovation.
08/2018	New arxiv preprint available on Faster PET Reconstruction with Non-Smooth Priors by Randomization and Preconditioning. This is an all UK collaboration with Pawel Markiewicz from UCL and Carola-Bibiane Schönlieb from Cambridge.
08/2018	Our paper on Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications has been accepted for publication at SIAM Optimization.
07/2018	A new preprint on A geometric integration approach to nonsmooth, nonconvex optimisation is now available on arXiv. This is joint work with Erlend Riis, Carola-Bibiane Schönlieb from Cambridge, UK and Reinout Quispel from Melbourne, Australia.
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].
03/2018	I accepted an offer to become a prize fellow with the Institute for Mathematical Innovation at the University of Bath. I am very excited to join them in September 2018.
03/2018	Our paper Blind image fusion for hyperspectral imaging with the directional total variation has been accepted for publication in Inverse Problems.

2017

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 Applications 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.

2016

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.

PostDocs

Jarrod Williams (2019-, machine learning, imaging; part of Faraday grant: Imaging Dynamic Electrochemical Interfaces)
Claire Delplancke (2020-, optimisation, PET imaging; part of EPSRC grant: PET++)

PhD Students

Ferdia Sherry, Cambridge (2016-, machine learning, imaging; co-supervisor with Carola-Bibiane Schönlieb)
Eric Baruch Gutiérrez Castillo, Bath (2019-, optimisation; primary supervisor)
Margaret Duff, Bath (2019-, machine learning, imaging; primary supervisor with Neill Campbell)

Further Students

Samual Cortinhas, summer student (funded by LMS and IMI), Bath (06-07/2019, magnetic resonance fingerprinting)
Varun Chhabra, master student, Bath (10/2018-04/2019, machine learning)
Alice Smiddy, master student, Bath (10/2018-02/2019, machine learning)
Georg Maierhofer, summer student (funded by LMS), Cambridge (06-08/2016, now PhD student at Cambridge, sampling for MRI; with Martin Benning and Carola-Bibiane Schönlieb)
Chris Irving, summer student (funded by SUROP), Cambridge (06-08/2016, now PhD student at Oxford, public outreach: image fusion photobox; with Martin Benning, Veronica Corona and Carola-Bibiane Schönlieb)
Emile Okada, summer student (funded by SUROP), Cambridge (06-08/2016, now PhD student at Oxford, public outreach: shadow tomography; with Martin Benning, Veronica Corona and Carola-Bibiane Schönlieb)

Visitors

Alessandro Perelli, Technical University of Denmark, Denmark (09/2019)
Konstantin Mishchenko, KAUST, Saudi Arabia (06/2019)
Evelyn Cueva, University of Chile, Santiago, Chile (11/2018-03/2019)