UCL Centre for Inverse Problems
We develop mathematical, computational, and statistical tools to uncover hidden causes in complex data, powering breakthroughs in imaging, AI, scientific discovery and decision-making.
Our research
The UCL Centre for Inverse Problems advances the theory and practical use of inverse problems – where the aim is to uncover hidden causes from the data we can observe. These problems underpin many advances in modern science and engineering, helping improve medical diagnosis, environmental monitoring, industrial safety, and the modelling tools that support future research.
Our work is organised around several key areas.
Mathematical foundations
We develop the mathematical theory needed to make inverse problems reliable and useful. Many such problems are ill-posed, meaning small errors in the data can lead to large changes in the result. We focus on regularisation techniques, variational methods, and optimal control approaches to stabilise solutions and ensure they reflect physical reality. This foundational work supports progress across science, engineering, and data-intensive fields.
Computational imaging
We design state-of-the-art algorithms that turn noisy or incomplete measurements into clear images. This is essential in medical imaging – such as CT, MRI, and photoacoustic imaging – where improved reconstructions can support earlier diagnosis and safer treatments. Our methods also help reveal hidden structures in geophysical exploration and industrial inspection.
Machine learning integration
We investigate how deep learning can be combined with classical inverse problem techniques. Machine learning excels at spotting patterns in data, while traditional approaches offer physical interpretability. Blending the two creates reconstruction tools that are more accurate, more robust, and better suited to real-world conditions. This hybrid approach is opening new directions in imaging, simulation, and scientific analysis.
Statistical inference and uncertainty quantification
Inverse problems often have multiple plausible solutions. We develop probabilistic and Bayesian methods that quantify uncertainty and show how confident we can be in a result. This is crucial in applications such as climate science, where sound evidence guides policy, and in any setting where decisions rely on imperfect or incomplete measurements.
Visual computing and 3D reconstruction
We study how to recover shape, movement, and appearance from visual data. This includes computer vision and 3D modelling techniques with uses in robotics, healthcare, and digital media. Our work helps systems interpret complex environments more reliably and enables richer digital representations for research and industry.
High-performance scientific computing
Large inverse problems require significant computational power. We create scalable numerical methods – including finite and boundary element approaches, parallel solvers, and domain decomposition techniques – that allow researchers to run complex simulations efficiently. These tools are vital for advances in physics, engineering, and astronomy, where detailed models deepen scientific understanding and drive technological innovation.
Selected Publications
Our research is published in leading journals and international conferences across inverse problems, imaging, and machine learning.
- Altamirano, Matias, Francois-Xavier Briol, and Jeremias Knoblauch . ‘Robust and Conjugate Gaussian Process Regression’. Proceedings of Machine Learning Research 235 (2024): 1155–85. https://proceedings.mlr.press/v235/altamirano24a.html.
- Arridge, S R. ‘Optical Tomography in Medical Imaging’. Inverse Problems 15, no. 2 (April 1999): R41–93. https://doi.org/10.1088/0266-5611/15/2/022.
- Barbano, Riccardo, Alexander Denker, Hyungjin Chung, Tae Hoon Roh, Simon Arridge, Peter Maass, Bangti Jin, and Jong Chul Ye. ‘Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstruction’. IEEE Transactions on Medical Imaging 44, no. 5 (May 2025): 2093–104. https://doi.org/10.1109/TMI.2024.3524797.
- Benning, Martin, and Martin Burger. ‘Modern Regularization Methods for Inverse Problems’. Acta Numerica 27 (May 2018): 1–111. https://doi.org/10.1017/S0962492918000016.
- Burman, Erik, Mihai Nechita, and Lauri Oksanen. ‘Optimal Approximation of Unique Continuation’. Foundations of Computational Mathematics 25, no. 3 (June 2025): 1025–45. https://doi.org/10.1007/s10208-024-09655-w.
- Burman, Erik, Mihai Nechita, and Lauri Oksanen. ‘Unique Continuation for the Helmholtz Equation Using Stabilized Finite Element Methods’. Journal de Mathématiques Pures et Appliquées 129 (September 2019): 1–22. https://doi.org/10.1016/j.matpur.2018.10.003.
- Cai, Xiaohao, Jason D. McEwen, and Marcelo Pereyra. ‘Proximal Nested Sampling for High-Dimensional Bayesian Model Selection’. Statistics and Computing 32, no. 5 (October 2022): 87. https://doi.org/10.1007/s11222-022-10152-9.
- Charita, Dellaporta, Jeremias Knoblauch, Theodoros Damoulas, and François-Xavier Briol. ‘Robust Bayesian Inference for Simulator-Based Models via the MMD Posterior Bootstrap’. Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, 2022, 943–70.
- Denker, Alexander, Francisco Vargas, Shreyas Padhy, Kieran Didi, Simon Mathis, Riccardo Barbano, Vincent Dutordoir, Emile Mathieu, Urszula Julia Komorowska, and Pietro Lio. ‘DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised $ h $-Transform’. Advances in Neural Information Processing Systems 37 (2024): 19636–82.
- Duff, M. A. G., N. D. F. Campbell, and M. J. Ehrhardt. ‘Regularising Inverse Problems with Generative Machine Learning Models’. Journal of Mathematical Imaging and Vision 66, no. 1 (January 2024): 37–56. https://doi.org/10.1007/s10851-023-01162-x.
- Duff, M A G, I J A Simpson, M J Ehrhardt, and N D F Campbell. ‘VAEs with Structured Image Covariance Applied to Compressed Sensing MRI’. Physics in Medicine & Biology 68, no. 16 (August 2023): 165008. https://doi.org/10.1088/1361-6560/ace49a.
- Ehrhardt, Matthias J, Željko Kereta, Jingwei Liang, and Junqi Tang. ‘A Guide to Stochastic Optimisation for Large-Scale Inverse Problems’. Inverse Problems 41, no. 5 (May 2025): 053001. https://doi.org/10.1088/1361-6420/adc0b7.
- Hauptmann, Andreas, Felix Lucka, Marta Betcke, Nam Huynh, Jonas Adler, Ben Cox, Paul Beard, Sebastien Ourselin, and Simon Arridge. ‘Model-Based Learning for Accelerated, Limited-View 3-D Photoacoustic Tomography’. IEEE Transactions on Medical Imaging 37, no. 6 (June 2018): 1382–93. https://doi.org/10.1109/TMI.2018.2820382.
- Jin, Bangti, and Željko Kereta. ‘On the Convergence of Stochastic Gradient Descent for Linear Inverse Problems in Banach Spaces’. SIAM Journal on Imaging Sciences 16, no. 2 (June 2023): 671–705. https://doi.org/10.1137/22M1518542.
- Kabri, Samira, Alexander Auras, Danilo Riccio, Hartmut Bauermeister, Martin Benning, Michael Moeller, and Martin Burger. ‘Convergent Data-Driven Regularizations for CT Reconstruction’. Communications on Applied Mathematics and Computation 6, no. 2 (June 2024): 1342–68. https://doi.org/10.1007/s42967-023-00333-2.
- Mars, Matthijs, Marta M Betcke, and Jason D McEwen. ‘Learned Radio Interferometric Imaging for Varying Visibility Coverage’. RAS Techniques and Instruments 4 (January 2025): rzaf025. https://doi.org/10.1093/rasti/rzaf025.
- Price, M A, J D McEwen, L Pratley, and T D Kitching. ‘Sparse Bayesian Mass-Mapping with Uncertainties: Full Sky Observations on the Celestial Sphere’. Monthly Notices of the Royal Astronomical Society 500, no. 4 (December 2020): 5436–52. https://doi.org/10.1093/mnras/staa3563.
- Xie, Xinheng, Yue Wu, Hao Ni, and Cuiyu He. ‘NODE-Imgnet: A PDE-Informed Effective and Robust Model for Image Denoising’. SSRN Electronic Journal, ahead of print, 2023. https://doi.org/10.2139/ssrn.4473320.
Our People
| Name | Job Title | |
| Prof Lourdes Agapito | l.agapito@ucl.ac.uk | Professor of 3D Vision |
| Associate Prof Kaan Aksit | k.aksit@ucl.ac.uk | Associate Professor Immersive Reality Systems |
| Prof Simon Arridge | s.arridge@ucl.ac.uk | Professor of Image Processing |
| Prof Martin Benning | martin.benning@ucl.ac.uk | Professor of Inverse Problems (Head of Centre) |
| Prof Marta Betcke | m.betcke@ucl.ac.uk | Professor of Scientific Computing |
| Prof Timo Betcke | t.betcke@ucl.ac.uk | Professor of Computational Mathematics |
| Prof Francois-Xavier Briol | f.briol@ucl.ac.uk | Professor of Statistics and Machine Learning |
| Prof Erik Burman | e.burman@ucl.ac.uk | Chair of Computational Mathematics |
| Prof Neill Campbell | neill.campbell@ucl.ac.uk | Professor of Inverse Problems |
| Prof Serge Guillas | s.guillas@ucl.ac.uk | Professor of Statistics |
| Associate Prof Max Jensen | max.jensen@ucl.ac.uk | Associate Professor in Applied Mathematics |
| Dr Zeljko Kereta | z.kereta@ucl.ac.uk | Senior Research Fellow |
| Prof Hao Ni | h.ni@ucl.ac.uk | Professor of Mathematics |
| Prof Jason McEwen | jason.mcewen@ucl.ac.uk | Professor of Astrostatistics and Astroinformatics |
| Postdocs | ||
| Dr Alexander Denker | a.denker@ucl.ac.uk | Research Fellow in the Mathematics of Deep Learning |
| Dr Riccardo Barbano | riccardo.barbano.19@ucl.ac.uk | Research Fellow in the Mathematics of Deep Learning |
Funding and partnerships
Our work is supported by major funders in the UK and beyond, including EPSRC, the Alan Turing Institute, ARIA, the Leverhulme Trust, and STFC. We collaborate with academic partners, research centres, and industry groups to advance imaging, modelling, and data-driven computation.
Selected funded projects
- Mathematics for Deep Learning – EPSRC (2022–2027)
- Transfer Learning for Monte Carlo Methods – EPSRC (2024–2027)
- Robust Foundations for Bayesian Inference – EPSRC (2024–2025)
- Bayesian Robustness in Filtering Algorithms – Alan Turing Institute (2024–2025)
- Centre for Doctoral Training in Data-Intensive Science – STFC (ongoing)
- Forecasting Tipping Points (VERIFY) – ARIA (from 2025)
- EPSRC CDT in Collaborative Computational Modelling – EPSRC (2024–2033)
Related programmes
The UCL Centre for Inverse Problems contributes to several major research and training initiatives across UCL. These programmes strengthen our work by linking inverse problem theory with advances in machine learning, data-intensive science, and scientific computing. Centre members teach, supervise, and collaborate across the following areas:
Maths4DL is an EPSRC-funded research programme that aims to build the mathematical foundations of deep learning. Centre members, including Co-Investigator Professor Simon Arridge, contribute to research on reliable and interpretable AI, helping connect inverse problems with modern machine learning theory.
The UCL ELLIS Unit forms part of the European Laboratory for Learning and Intelligent Systems (ELLIS), a leading network for machine learning and AI research. With Professor François-Xavier Briol as Co-Director, the Centre works closely with colleagues across Europe on projects at the interface of inverse problems and AI.
DISI brings together researchers working on large-scale data analysis in areas such as astrophysics, medical imaging, and industrial applications. Centre member Professor Jason McEwen is the incoming Director. Our collaboration with DISI and the associated STFC-funded CDT supports doctoral training and research in methods that draw on inverse problems, high-performance computing, and scientific data analysis.
The UCL Centre for Data Science connects researchers developing new mathematical, statistical, and computational methods for analysing complex datasets. Centre members contribute to seminars, collaborations, and joint research at the intersection of data science and inverse modelling across health, engineering, and the physical sciences.
The Centre for Doctoral Training in Collaborative Computational Modelling at the Interface (CCMI) is suited to students with strong backgrounds in mathematics, statistics, or computer science who wish to develop new computational and statistical approaches.
Work with us
The UCL Centre for Inverse Problems is a growing research community, and we welcome interest from prospective doctoral students, postdoctoral researchers, and academic or industrial partners.
If you are considering doctoral study with us, we encourage you to explore the research interests of our academic staff in the Our People section and identify a potential supervisor whose work aligns with your own.
For general guidance on entry requirements, applications, and funding routes, please refer to the UCL Graduate Study pages.
Funding is highly competitive, and several dedicated routes exist for students wishing to work with members of our Centre:
- Centre for Doctoral Training in Data Intensive Science (DISI) – for students interested in applying inverse problem methods to large-scale scientific experiments in areas such as astrophysics and cosmology.
- Centre for Doctoral Training in Collaborative Computational Modelling at the Interface (CCMI) – suited to students with strong backgrounds in mathematics, statistics, or computer science who wish to develop new computational and statistical approaches.
- UCL and departmental scholarships – including opportunities offered through Computer Science, Mathematics, Statistical Science, and central UCL schemes.
Once you have identified a potential supervisor and funding route, you are welcome to contact them directly to discuss your research interests.
We work closely with partners across academia, industry, and the public sector. If you are interested in collaborating with us – whether on mathematical modelling, computational imaging, statistical inference, or AI-driven approaches to inverse problems – please contact Martin Benning.
