About me
I am a Reader at the Department of Mathematical Sciences, University of Bath.
I am the deputy director of the  EPSRC Programme Grant on the Mathematics for Deep Learning, co-director of the Centre for Mathematics and Algorithms for Data (MAD) and heading the Bath Imaging Group.
I am also a fellow of the Institute for Mathematical Innovation.
    
My research lies broadly on the interface of optimization, inverse imaging problems and machine learning. My work bridges mathematical theory to various applications including medical imaging, material sciences, biology and geophysics.
Contactm.ehrhardt@bath.ac.uk
Office: 6 West, 1.08

University of Bath

Bath BA2 7JU

United Kingdom

News

10/2023	Our paper on Regularising Inverse Problems with Generative Machine Learning Models got published by the Journal of Mathematical Imaging and Vision. This is joint work with Margaret Duff (STFC, UK) and Neill Campbell (Bath, UK).
08/2023	New preprint: Dynamic Bilevel Learning with Inexact Line Search. Joint work with Mohammad Sadegh Salehi (Bath, UK), Subhadip Mukherjee (Kharagpur, India) and Lindon Roberts (Sydney, Australia).
07/2023	Congratulations to Eric Baruch Gutiérrez Castillo for completing his PhD!
07/2023	Our paper on VAEs with structured image covariance applied to compressed sensing MRI got accepted by IOP Phyics in Medicine and Biology. This is joint work with Margaret Duff (STFC, UK), Neill Campbell (Bath, UK) and Ivor Simpson (Sussex, UK).
07/2023	New preprint: Proximal Langevin Sampling With Inexact Proximal Mapping. Joint work with Lorenz Kuger (DESY Hamburg, Germany) and Carola-Bibiane Schönlieb (Cambridge, UK).
07/2023	New preprint: Designing Stable Neural Networks using Convex Analysis and ODEs. Joint work with Elena Celledoni, Davide Murari, Brynjulf Owren (all NTNU, Norway), Carola-Bibiane Schönlieb and Ferdia Sherry (both Cambridge, UK).
05/2023	New preprint: On Optimal Regularization Parameters via Bilevel Learning. Joint work with Seb Scott and Silvia Gazzola (both Bath, UK).
03/2023	Congratulations to Margaret Duff for completing her PhD!
03/2023	We are looking for excellent candidates to join our team on image reconstruction as a PhD student. If you are interested, please find more information here.
01/2023	New preprint: Stochastic Primal Dual Hybrid Gradient Algorithm with Adaptive Step-Sizes, Joint work with Antonin Chambolle (Paris-Dauphine, France), Claire Delplancke (Bath, UK), Carola-Bibiane Schönlieb and Junqi Tang (both Cambridge, UK).
01/2023	New preprint: Uncertainty Quantification in CT pulmonary angiography. Joint work with Adwaye Rambojun (Bath, UK), Hend Komber, Jennifer Rossdale, Jay Suntharalingam, Jonathan Rodrigues (all Royal United Hospital, Bath, UK) and Audrey Repetti (Heriott Watt, UK).
01/2023	New preprint: Analyzing Inexact Hypergradients for Bilevel Learning. Joint work with Lindon Roberts (Sydney, Australia).
11/2022	We were awarded the John Ockendon Prize of the European Journal of Applied Mathematics for our paper on Structure-preserving deep learning.
10/2022	New preprint: Compressed Sensing MRI Reconstruction Regularized by VAEs with Structured Image Covariance. This is joint work with Margaret Duff, Neill Campbell (both Bath, UK) and Ivor Simpson (Sussex, UK).
10/2022	I joined the new founded AIMS journal on Applied Mathematics for Modern Challenges (AMMC) as an Associate Editor. The focus of the journal is to on real world applications of applied mathematics.
09/2022	Our paper on Imaging with Equivariant Deep Learning has been accepted by the IEEE Signal Processing Magazine. It is also available on arxiv. This is joint work with Dongdong Chen (U Edinburgh, UK), Mike Davies (U Edinburgh, UK), Carola-Bibiane Schönlieb (Cambridge, UK), Ferdia Sherry (Cambridge, UK), Julián Tachella (Lyon, France).
07/2022	New preprint out On the convergence and sampling of randomized primal-dual algorithms and their application to parallel MRI reconstruction. This is joint work with Eric B. Gutierrez (Bath, UK) and Claire Delplancke (Bath, UK).
06/2022	New preprint out on Regularization of Inverse Problems: Deep Equilibrium Models versus Bilevel Learning. This is joint work with Danilo Riccio and Martin Benning (both Queen Mary, UK).
05/2022	I was selected to join the EPSRC Mathematical Sciences Early Career Forum. A key aim of the forum is to act as an informal advisory stream regarding EPSRC’s mathematical sciences strategy.
05/2022	Huge congratulations to Claire Deplancke who won the 2022 CoSeC Impact Award!
03/2022	The opening workshop of our EPSRC Programme Grant on the Mathematics of Deep Learning will take place on 21/22 April in Bath with the option to virtually join in. Some more information is available here.
03/2022	Our paper on Enhancing the spatial resolution of hyperpolarized carbon‐13 MRI of human brain metabolism using structure guidance was the No 1 Pick for March by the Editor of Magnetic Resonance in Medicine. Always good to see when people like your research!
03/2022	I am co-organizing with Daniel Lesnic (Leeds) a special issue on "The Applied Mathematics of Machine Learning" for IMA Journal of Applied Mathematics. Please let me know if you are interested in submitting to our special issue.
01/2022	Our programme grant on the Mathematics of Deep Learning just started! Looking forward to 5 years of exciting research. See here for more details.

News archive:

2021

11/2021	Want to do a PhD with me on inverse problems and machine learning? We are always looking for talented students! You can find more information for a current project with Mohammad Golbabaee (Bath Computer Science, UK) here.
10/2021	I am a guest editor at IOP Inverse Problems for a special issue on Big Data Inverse Problems. The other guest editors are Matthias Chung (Virginia Tech, US) and Carola-Bibiane Schönlieb (Cambridge, UK). The deadline for papers is 31 July, 2022.
10/2021	Our paper on Enhancing the spatial resolution of hyperpolarized carbon‐13 MRI of human brain metabolism using structure guidance was published in Magnetic Resonance in Medicine. This is joint work with Ferdia Gallagher, Mary McLean and Carola-Bibiane Schönlieb (all Cambridge, UK).
10/2021	Congratulations to Ferdia Sherry for passing his PhD viva with minor corrections!
10/2021	My new contract as a Reader in the Department of Mathematical Sciences at the University Bath just became effective. Really looking forward to more productive years to come!
07/2021	Paper published: Our paper on Equivariant neural networks for inverse problems was published in IOP Inverse Problems. This is joint work with Elena Celledoni, Brynjulf Owren (both NTNU, Norway), Christian Etmann, Carola-Bibiane Schönlieb and Ferdia Sherry (all Cambridge, UK).
07/2021	Our paper on A geometric integration approach to nonsmooth, nonconvex optimisation got published in Foundations of Computational Mathematics. This is joint work with Erlend Riis, Carola-Bibiane Schönlieb (both Cambridge, UK) and Reinout Quispel (Melbourne, Australia).
07/2021	New preprint out on Regularising Inverse Problems with Generative Machine Learning Models. This is joint work with Margaret Duff and Neill Campbell (both Bath, UK).
07/2021	Our paper on Synergistic Multi-spectral CT Reconstruction with Directional Total Variation got published in the Philosophical Transactions A of the Royal Society. This is joint work with Evelyn Cueva (Escuela Politecnica Nacional and Universidad Tecnica de Cotopaxi, both Ecuador), Alexander Meaney (Helsinki, Finland) and Samuli Siltanen (Helsinki, Finland).
07/2021	Our paper on Motion estimation and correction for simultaneous PET/MR using SIRF and CIL got published in the Philosophical Transactions A of the Royal Society. This is joint work with many people from CCP SyneRBI, in particular Richard Brown (KCL, UK) and Kris Thielemans (UCL, UK).
05/2021	New book chapter out on Multi-modality Imaging with Structure-Promoting Regularizers as part of the Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. This is a good starting point if you are interested in multi-modality imaging and guided image reconstruction.
05/2021	Our paper out on efficient algorithms for supervised machine learning for inverse problems (bilevel learning) Inexact Derivative-Free Optimization for Bilevel Learning has been published by the Journal of Mathematical Imaging and Vision. This is joint work with Lindon Roberts (ANU, Australia).
05/2021	Need an introduction to synergistic image reconstruction for multi-modality imaging? Check out our recent review paper on (An overview of) Synergistic reconstruction for multimodality/multichannel imaging methods. This is joint work with Simon Arridge and Kris Thielemans (both UCL, UK).
05/2021	New paper out on Convergence Properties of a Randomized Primal-Dual Algorithm with Applications to Parallel MRI. This is joint work with Eric B. Gutierrez (Bath, UK) and Claire Delplancke (Bath, UK). It will be presented by Eric at Scale Space and Variational Methods in Computer Vision.
03/2021	Our Progamme Grant on the Mathematics of Deep Learning got funded by the EPSRC. Very excited about our 5-year project starting in January 2022 with Chris Budd (Bath, UK), Simon Arridge (UCL, UK), Bangti Jin (UCL, UK), Carola-Bibiane Schönlieb (Cambridge, UK)and Richard Nickl (Cambridge, UK).
02/2021	New preprint out on Equivariant neural networks for inverse problems. This is joint work with Elena Celledoni (NTNU, Norway), Christian Etmann (Cambridge, UK), Brynjulf Owren (NTNU, Norway), Carola-Bibiane Schönlieb (Cambridge, UK) and Ferdia Sherry (Cambridge, UK).
01/2021	New preprint out on Synergistic Multi-spectral CT Reconstruction with Directional Total Variation. This is joint work with Evelyn Cueva (Escuela Politecnica Nacional and Universidad Tecnica de Cotopaxi, both Ecuador), Alexander Meaney (Helsinki, Finland) and Samuli Siltanen (Helsinki, Finland).

2020

12/2020	Our paper Robust Image Reconstruction with Misaligned Structural Information got published by IEEE Access. This is joint work with Leon Bungert (Erlangen, Germany).
11/2020	Our paper on Efficient Hyperparameter Tuning with Dynamic Accuracy Derivative-Free Optimization got accepted to the NeurIPS 2020 workshop OPT2020: Optimization for Machine Learning. This is joint work with Lindon Roberts (ANU, Australia).
10/2020	New preprint out on faster reconstruction for Magnetic Resonance Fingerprinting, see link. This is joint work with my student Sam Cortinhas and Mohammad Golbabaee (Bath).
09/2020	Our paper on Accelerating Variance-Reduced Stochastic Gradient Methods got accepted by Mathematical Programming. This is joint work with Derek Driggs and Carola-Bibiane Schönlieb (both Cambridge, UK).
08/2020	Our paper on Learning the Sampling Pattern for MRI got accepted by IEEE Transactions on Medical Imaging. 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).
07/2020	Alberto Paganini and I are organising an LMS-workshop on Imaging meets Computational PDEs. Please sign up here if you want to attend.
07/2020	New review paper out on Multi-modality imaging with structure-promoting regularisers. If you are new to image reconstruction from multi-modality imaging data, this is the best place to start!
06/2020	New paper out on efficient algorithms for supervised machine learning for inverse problems: Inexact Derivative-Free Optimization for Bilevel Learning. This is joint work with Lindon Roberts (ANU, Australia).
05/2020	New paper out on Structure preserving deep learning. In this paper we review several connections between deep learning and mathematical fields like numerical analyis, optimal control and inverse problems. This is joint work with Elena Celledoni (NTNU, Norway), Christian Etmann (Cambridge, UK), Robert McLachlan (Massey University, New Zealand), Brynjulf Owren (NTNU, Norway), Carola-Bibiane Schönlieb (Cambridge, UK) and Ferdia Sherry (Cambridge, UK).
04/2020	Congratulations to my PhD student Margaret Duff who was awarded a Doctoral Recognition Award. Only 14 such awards were handed out to PhD students in Bath this year.
04/2020	Glad to be named an "outstanding reviewer" for IOP Inverse Problems.
04/2020	New paper out on making structure-promoting regularizers robust to misalignment: Robust Image Reconstruction with Misaligned Structural Information. This is joint work with Leon Bungert (Erlangen, Germany).
03/2020	We got awarded a "collaborative computational project" (CCP) on Synergistic Reconstruction for Biomedical Imaging by EPSRC. The aim is to develop a software framework to support multi-modality imaging, e.g. PET-MR, SPECT-CT. Lead by Kris Thielemans (UCL), the project includes a wide UK network: David Atkinson (UCL), me (Bath), Julian Matthews (Manchester), Andrew Reader (KCL) and Charalampos "Harry" Tsoumpas (Leeds). This project's predecessor was CCP PET-MR.
02/2020	Congratulations to Samuel Cortinhas. He was invited to present his work that he did with me in summer 2019 at this year's Posters in Parliament as part of the British Conference of Undergraduate Research (BCUR). Here you can read more about it.
01/2020	Congratulations to my PhD 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.

2019

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.

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).
11/2018	Congratulations to my PhD student Ferdia Sherry who won the Best Poster Award at the Cantab Capital Institute for the Mathematics of Information -- Connecting with Industry.
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.

BIG: Bath Imaging Group

Lead

Matthias J. Ehrhardt

PostDocs

Pawel Markiewicz (2022-, optimisation, PET imaging; part of EPSRC grant: PET++)
Hok Shing Wong (2022-, machine learning; part of EPSRC grant: m4DL)

PhD Students

Patrick Fahy (2023-, machine learning, inverse problems; lead supervisor with Mohammad Golbabaee)
Mohammad Sadegh Salehi (2022-, machine learning, optimization; lead supervisor with Subhadip Mukherjee)
Pablo Arratia (2022-, machine learning, inverse problems; lead supervisor with Lisa Kreusser)
Seb Scott (2021-, machine learning, inverse problems; lead supervisor with Silvia Gazzola)
Eric Baruch Gutiérrez Castillo (2019-, optimisation; lead supervisor)

Former members

Margaret Duff (2019-23, machine learning, imaging; lead supervisor with Neill Campbell; then researcher at STFC)
Marco Mauritz, University of Muenster, Germany (visitor, 11/2022-01/2023)
Claire Delplancke (PostDoc 2020-2022, optimisation, PET imaging, part of EPSRC grant: PET++; then research engineer at EDF)
Jarrod Williams (PostDoc 2019-2021, machine learning, imaging, part of Faraday grant: Imaging Dynamic Electrochemical Interfaces; then PostDoc in computer science at Bath)
Ferdia Sherry (PhD student 2016-2021 in Cambridge, machine learning, imaging, co-supervisor with Carola-Bibiane Schönlieb; then PostDoc in Cambridge)
Alessandro Perelli, Technical University of Denmark, Denmark (visitor, 09/2019)
Samual Cortinhas, summer student (funded by LMS and IMI) (06-07/2019, magnetic resonance fingerprinting; then Part III in mathematics at Cambridge)
Konstantin Mishchenko, KAUST, Saudi Arabia (visitor, 06/2019)
Evelyn Cueva, University of Chile, Santiago, Chile (visitor, 11/2018-03/2019)
Varun Chhabra, master student (10/2018-04/2019, machine learning)
Alice Smiddy, master student (10/2018-02/2019, machine learning)
Georg Maierhofer, summer student (funded by LMS), Cambridge (06-08/2016, sampling for MRI, with Martin Benning and Carola-Bibiane Schönlieb; then PhD student at Cambridge)
Chris Irving, summer student (funded by SUROP), Cambridge (06-08/2016, public outreach: image fusion photobox; with Martin Benning, Veronica Corona and Carola-Bibiane Schönlieb; then PhD student at Oxford)
Emile Okada, summer student (funded by SUROP), Cambridge (06-08/2016, public outreach: shadow tomography; with Martin Benning, Veronica Corona and Carola-Bibiane Schönlieb; then PhD student at Oxford)

Are you interested in working with me on inverse problems, machine learning, mathematical imaging or optimization? I am happy to support fellowship applications including but not limited to the Marie-Curie Fellowship, EPSRC Doctoral Prize/Postdoctoral Fellowship, LMS Early Career Fellowship, or Leverhulme Early Career Fellowship, see link for more details. I am also interested in supervising PhD students on these topics. Please check out SAMBa if you are interested.

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