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Faculty of Mathematics



  • from 09/16:  Leverhulme Early Career Fellow, DAMTP, University of Cambridge
  • 04/15-08/16: Postdoctoral Research Associate, DAMTP, University of Cambridge
  • 10/14-03/15: Associate Professor (Temporarily), MIC, Universität zu Lübeck, Germany
  • 09/12-09/14: Postdoctoral Research Associate, MRRC, CEB, University of Cambridge
  • 07/11-08/12: Postdoctoral Research Associate, Westfälische Wilhelms-Universität, Münster
  • 07/08-06/11: Phd Student, Westfälische Wilhelms-Universität, Münster, Germany

Short biography

Martin Benning is a Leverhulme Trust Early Career Fellow supported by the Isaac Newton Trust, and member of the Cambridge Image Analysis group of Dr Carola-Bibiane Schönlieb. With his work on singular regularisation of inverse problems he obtained his doctoral degree at the University of Münster, Germany, under supervision of Prof. Martin Burger. His current research focuses on inverse problem theory, non-smooth variational regularisation methods, convex- & non-convex optimisation techniques and machine learning. His main applications of interest are Magnetic Resonance Imaging (MRI), Electron Tomography (both from incomplete measurments) and Positron Emission Tomography (PET).

Publications (selection)

  • MB, Guy Gilboa, Carola-Bibiane Schönlieb. "Learning parametrised regularisation functions via quotient minimisation." Proceedings in Applied Mathematics and Mechanics 16(1) (2016): 933-936.
  • MB, Florian Knoll, Carola-Bibiane Schönlieb, and Tuomo Valkonen. "Preconditioned ADMM with nonlinear operator constraint." Accepted for publication in IFIP Advances in Information and Communication Technology (2016).

Accepted preprint for publicationcode

  • Michael Möller, MB, Carola-Bibiane Schönlieb, and Daniel Cremers. "Variational depth from focus reconstruction." Image Processing, IEEE Transactions on Image Processing 24, no. 12 (2015): 5369-5378.
  • MB, Lynn Gladden, Daniel Holland, Carola-Bibiane Schönlieb, and Tuomo Valkonen. "Phase reconstruction from velocity-encoded MRI measurements–a survey of sparsity-promoting variational approaches." Journal of Magnetic Resonance 238 (2014): 26-43.

  • MB, and Martin Burger. "Ground states and singular vectors of convex variational regularization methods." Methods and Applications of Analysis  20, no. 4 (2013): 295-334

  • Martin Burger, Michael Möller, MB, and Stanley Osher. "An adaptive inverse scale space method for compressed sensing." Mathematics of Computation 82, no. 281 (2013): 269-299.
  • MB, Christoph Brune, Martin Burger, and Jahn Müller. "Higher-order TV methods—enhancement via Bregman iteration." Journal of Scientific Computing 54, no. 2-3 (2013): 269-310.

  • MB, and Martin Burger. "Error estimates for general fidelities." Electronic Transactions on Numerical Analysis 38, no. 44-68 (2011): 77.

A complete list of publications can be found on my Google scholar page.


I was lecturing on Inverse Proplems in Imaging together with Matthias J. Ehrhardt during Michaelmas term 2016. Information and course materials were provided here.

I was lecturing on Inverse Problems during Michaelmas term 2015. The lecture was Tuesdays and Thursdays, 9 am, starting on October 8th and ending on December 1st. Some of the course materials are still available here:

Lecture notes (will constantly be updated - current state: 22.12.15, 5:30 pm)

Exercise sheet 1 (has been presented on October 23rd, 3 pm, MR11)

Exercise sheet 2 (will be presented on November 13th, 3 pm, MR5)

Exercise sheet 3 (will be presented on November 27th, 1.30 pm, MR5)


Phase diagrams of liquid-phase mixing in multi-component metal-organic framework glasses constructed by quantitative elemental nano-tomography
SM Collins, KE MacArthur, L Longley, R Tovey, M Benning, CB Schönlieb, TD Bennett, PA Midgley
– APL Materials
Enhancing joint reconstruction and segmentation with non-convex Bregman iteration
V Corona, M Benning, MJ Ehrhardt, LF Gladden, R Mair, A Reci, AJ Sederman, S Reichelt, CB Schönlieb
– Inverse Problems
Directional Sinogram Inpainting for Limited Angle Tomography
R Tovey, M Benning, C Brune, MJ Lagerwerf, SM Collins, RK Leary, PA Midgley, CB Schönlieb
– Inverse Problems
Inverse scale space decomposition
MF Schmidt, M Benning, CB Schönlieb
– Inverse Problems
Modern Regularization Methods for Inverse Problems
M Benning, M Burger
– Acta Numerica
Entropic Comparison of Atomic-Resolution Electron Tomography of Crystals and Amorphous Materials
SM Collins, RK Leary, PA Midgley, R Tovey, M Benning, C-B Schönlieb, P Rez, MMJ Treacy
– Physical review letters
Nonlinear spectral image fusion
M Benning, M Möller, RZ Nossek, M Burger, D Cremers, G Gilboa, CB Schönlieb
– Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
10302 LNCS,
Learning Filter Functions in Regularisers by Minimising Quotients
M Benning, G Gilboa, JS Grah, CB Schönlieb
– Lecture Notes in Computer Science
10302 LNCS,
Learning parametrised regularisation functions via quotient minimisation
M Benning, G Gilboa, C-B Schönlieb
– Proceedings in Applied Mathematics and Mechanics
Fast imaging of laboratory core floods using 3D compressed sensing RARE MRI.
NP Ramskill, I Bush, AJ Sederman, MD Mantle, M Benning, BC Anger, M Appel, LF Gladden
– J Magn Reson
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Research Groups

Cantab Capital Institute for the Mathematics of Information
Centre for Mathematical Imaging in Healthcare


01223 760449