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School of Mathematical Sciences

Dr Martin Benning


Senior Lecturer in Inverse Problems and Machine Learning, Director of the Information and Computational Science BSc programme

Telephone: +44 (0)20 7882 5370
Room Number: Mathematical Sciences Building, Room: MB-512
Office Hours: On request


Dr Martin Benning is a Senior Lecturer in Inverse Problems and Machine Learning, member of the Statistics and Data Science group, member of the Centre for Mathematical Foundations of Artificial Intelligence (MFAI) and Research Fellow at the Digital Environment Research Institute (DERI). He is also Turing Fellow at the Alan Turing Institute and Director of the Information and Computational Science (ICS) BSc programme at Queen Mary School Hainan.

Dr Benning's area of mathematical expertise is the theoretical and computational handling of inverse & ill-posed problems. In inverse problems, an unknown quantity – such as the image of the interior of a human body – is only accessible indirectly through the inversion of a mathematical operator. In nearly all relevant applications, this inversion process is highly unstable with respect to measurement errors. A remedy is the approximation of the inverses via families of continuous operators, also known as regularisation operators.

The particular focus of Dr Benning's research is the analysis and numerical realisation of regularisation operators arising from the minimisation of non-smooth functionals. His research covers topics such as non-linear (numerical) analysis, (convex and non-convex) optimisation, functional analysis, machine learning, imaging and image processing, compressed sensing and (big) data analysis.


Research Interests:

  • Inverse problems
  • Machine learning
  • Optimisation
  • Imaging
  • Numerical analysis
  • Variational calculus
  • Regularisation theory
  • Compressed sensing

Examples of research funding:

Leverhulme Trust Early Career Fellowship "Learning from mistakes: a supervised feedback-loop for imaging applications" (September 2016 - August 2019)


 Selected publications:

  • M. Benning, M. M. Betcke, M. J. Ehrhardt, and C.-B. Schönlieb. "Choose your path wisely: gradient descent in a Bregman distance framework." SIAM Journal on Imaging Sciences (2021), 14(2): 814-843
  • M. Benning, and E. S. Riis. “Bregman methods for large-scale optimisation with applications in imaging.” Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision (2021): 1-42
  • F. Sherry, M. Benning, J. C. De los Reyes, M. J. Graves, G. Maierhofer, G. Williams, C.-B. Schönlieb and M. J. Ehrhardt. “Learning the sampling pattern for MRI”. IEEE Transactions on Medical Imaging, 2020, 39(12): 4310-4321.
  • M. Benning, E. Celledoni, M. J. Ehrhardt, B. Owren, and C.-B. Schönlieb. “Deep learning as optimal control problems: Models and numerical methods.” Journal of Computational Dynamics, 2019, 6(2):171-198.
  • M. Benning, M. Burger. “Modern regularization methods for inverse problems”. Acta Numerica, 27, 1-111.
  • M. Benning, M. Möller, R. Nossek, M. Burger, D. Cremers, G. Gilboa, C. Schönlieb. “Nonlinear spectral image fusion”,SSVM 2017 proceedings, pages 41-53, volume 10302
  • M. Möller, M. Benning, C. Schönlieb, D. Cremers. „Variational depth from focus reconstruction. In: IEEE Transactions on Image Processing”, pages 5369–5378, volume 24(12)
  • M. Benning, L. Gladden, D. Holland, C. Schönlieb, T. Valkonen, “Phase reconstruction from velocity-encoded MRI measurements – a survey of sparsity-promoting variational approaches”,Journal of Magnetic Resonance, pages 26-43, volume 238
  • M. Benning, M. Burger, "Ground States and Singular Vectors of Convex Variational Regularization Methods", Methods and Applications of Analysis, pages 295-334, volume 20(4)
  • M. Benning, M. Burger, C. Brune, J. Müller, "Higher-Order TV Methods: Enhancement via Bregman Iteration", Journal of Scientific Computing, pages 1-42, volume 54(2-3)
  • M. Burger, M. Möller, M. Benning, S. Osher, "An Adaptive Inverse Scale Space Method for Compressed Sensing",Mathematics of Computation, pages 269-299, volume 82

For a full list of publications please visit my google scholar page or my public orcid profile.

Public Engagement

Marianne Freiberger wrote an article in the Plus Magazine on our work on nonlinear spectral image fusion.

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