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Faculty of Mathematics


Professor Schönlieb is Professor of Applied Mathematics at DAMTP and head of the Cambridge Image Analysis group (CIA). Moreover, she is the Director of the Cantab Capital Institute for the Mathematics of Information and Director of the EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging, a Fellow of Jesus College, Cambridge and co-leader of the IMAGES network. 




  • since October 2018: Professor at DAMTP, University of Cambridge, UK.
  • October 2015 to September 2018: Reader at DAMTP, University of Cambridge, UK.
  • since October 2011: Fellow of Jesus College, Cambridge, UK.
  • September 2010 to September 2015: Lecturer at DAMTP, University of Cambridge, UK.
  • September 2009 to September 2010: Postdoc at NAM (Institute of Numerical and Applied Mathematics), Georg-August University Goettingen, Germany.
  • October 2008 to September 2009: Research Assistant at DAMTP, University of Cambridge.
  • October 2005 to October 2008: Research Assistant at the Faculty of Mathematics, University of Vienna, Austria.
  • September 2002 to June 2004: Research Assistant at the Department of Mathematics, University of Salzburg, Austria.



  • July 18, 2009: Admission to the degree Doctor of Philosophy, University of Cambridge (UK)
  • January 30, 2004: Master’s degree in Mathematics with Honors, University of Salzburg (Austria)


Honors and Awards:

  • 2017: Philip Leverhulme Prize.
  • 2016: Whitehead Prize, London Mathematical Society.
  • 2013: EPSRC Science Photo Award, 1st Prize in the Category People.
  • 2008: Mary Bradburn Award from the BFWG.
  • 2004: Scholarship from the University of Salzburg (Austria) for exceptional achievements as a student
  • 2002: Hans-Stegbuchner-Award from the Department of Mathematics, University of Salzburg (Austria).


Dr Schönlieb's research interests range from nonlinear partial differential equations to computational- and convex analysis, with applications in digital image- and signal processing. She studies fourth-order equations and nonsmooth optimization problems, like the total variation functional, for image reconstruction, especially for what is called image inpainting. Moreover, she works on computational methods for large-scale problems appearing in 3- and 4-D imaging. Within this context she is interested in both the theoretical and numerical analysis of the problems considered as well as their practical implementation and their use for real-world applications like arts restoration and medical imaging. More details on CIA research see CIA research.

Selected Publications

  • M. Benning, L. Gladden, D. Holland, C.-B. Schönlieb, and T. Valkonen, Phase reconstruction from velocity-encoded MRI measurements - a survey of sparsity-promoting variational approaches , Journal of Magnetic Resonance 238 (2014), pp. 26--43.

  • L. Calatroni, B. Düring, and C.-B. Schönlieb, ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing, DCDS Series A, Special Issue for Arieh Iserles 65th birthday, 34(3), March 2014, pp. 931 - 957.

  • J. C. De Los Reyes, and C.-B. Schönlieb, Image denoising: Learning noise distribution via PDE-constrained optimisation, Inverse Problems and Imaging 7(4), pp. 1183--1214, November 2013. pdf DAMTP-Technical Report, NA2012/04

  • K. Papafitsoros, and C.-B. Schönlieb, A combined first and second order variational approach for image reconstruction, Journal of Mathematical Imaging and Vision, 48(2), pp. 308--338, 2014.

  • K. Papafitsoros, C.-B. Schönlieb, and B. Sengul, Combined first and second order total variation inpainting using split Bregman, in Image Processing On Line, vol. 2013, pp. 112-136.

  • F. Schubert, and C.-B. Schönlieb, Random Simulations for Generative Art Construction - Some Examples, Journal of Mathematics and the Arts, Vol. 7, Issue 1, 2013, pp. 29-39

  • A. Langer, S. Osher, and C.-B. Schönlieb, Bregmanized Domain Decomposition for Image Restoration, Journal of Scientific Computing, Vol. 54, Issue 2-3, pp. 549-576, 2013. UCLA-CAM report num. 11-30.

  • M. Fornasier, Y. Kim, A. Langer, and C.-B. Schönlieb, Wavelet Decomposition Method for L2/TV-Image Deblurring, SIAM J. Imaging Sci., Vol. 5, No. 3, 2012, pp. 857-885.

  • C. Gottschlich, C.-B. Schönlieb, Oriented Diffusion Filtering for Enhancing Low-quality Fingerprint Images, IET Biometrics, Vol. 1, No. 2, pp. 105-113, June 2012.

  • M. Burger, M. Franek, C.-B. Schönlieb, Regularised Regression and Density estimation based on Optimal Transport, Appl. Math. Res. Express 2012 (2), pp. 209-253.

  • C.-B. Schönlieb, A. Bertozzi, Unconditionally stable schemes for higher order inpainting, Communications in Mathematical Sciences Volume 9, Issue 2, pp. 413-457 (2011).

  • M. Fornasier, A. Langer, C.-B. Schönlieb, A convergent overlapping domain decomposition method for total variation minimization, Numerische Mathematik, Vol. 116, Nr. 4, pp. 645 - 685 (2010).

  • M. Burger, L. He, C.-B. Schoenlieb, Cahn-Hilliard inpainting and a generalization for grayvalue images, SIAM J. Imaging Sci. Volume 2, Issue 4, pp. 1129-1167 (2009), UCLA-CAM report num. 08-41.
  • M. Fornasier, C.-B. Schoenlieb, Subspace correction methods for total variation and l1- minimization, SIAM J. Numer. Anal. Nr. 47 Issue 5, pp. 3397-3428 (2009), arXiv:0712.2258v1 [math.NA].
  • C.-B. Schoenlieb, Total variation minimization with an H−1 constraint, CRM Series 9, Singularities in Nonlinear Evolution Phenomena and Applications proceedings, Scuola Normale Superiore Pisa 2009, pp. 201-232.
  • W. Baatz, M. Fornasier, P. Markowich, C.-B. Schoenlieb, Binary Based Fresco Restoration, Conference Proceedings of Bridges 2009, BANFF 2009, pp. 337-338.
  • J. D. Rossi, C.-B. Schoenlieb, Nonlocal higher order evolution equations, Applicable Analysis. Vol. 89(6), pp. 949-960, (2010).
  • J. Fernandez Bonder, J. D. Rossi, C.-B. Schoenlieb, The Best Constant and Extremals of the Sobolev Embeddings in Domains With Holes: the L∞ Case, Illinois Journal of Mathematics. Vol. 52(4), pp. 1111-1121, (2008).
  • M.Burger, S.-Y.Chu, P.Markowich, C.-B. Schoenlieb, The Willmore Functional and Instabilities in the Cahn-Hilliard equation, Communications in Mathematical Sciences, Volume 6, Issue 2 (June 2008), pp. 309-329, 2008.
  • J. Fernandez Bonder, J. D. Rossi, C.-B. Schoenlieb, An Optimization Problem Related to the Best Sobolev Trace Constant in Thin Domains, Communications in Contemporary Mathematics (CCM), Volume 10, Issue 5 (October 2008), pp. 633-650.



Analysis of Artifacts in Shell-Based Image Inpainting: Why They Occur and How to Eliminate Them
LR Hocking, T Holding, CB Schönlieb
– Foundations of Computational Mathematics
Variational Osmosis for Non-linear Image Fusion.
S Parisotto, L Calatroni, A Bugeau, N Papadakis, C-B Schonlieb
– CoRR
Mirror, Mirror, on the Wall, Who’s Got the Clearest Image of Them All?—A Tailored Approach to Single Image Reflection Removal
D Heydecker, G Maierhofer, AI Aviles-Rivero, Q Fan, D Chen, C-B Schonlieb, S Susstrunk
– IEEE Transactions on Image Processing
Faster PET reconstruction with non-smooth priors by randomization and preconditioning.
MJ Ehrhardt, P Markiewicz, C-B Schönlieb
– Phys Med Biol
Stability Analysis of Line Patterns of an Anisotropic Interaction Model
JA Carrillo, B During, LM Kreusser, CB Schonlieb
– SIAM Journal on Applied Dynamical Systems
RainFlow: Optical Flow under Rain Streaks and Rain Veiling Effect
R Li, R Tan, LF Cheong, A Aviles-Rivero, Q Fan, C Schoenlieb
Phase diagrams of liquid-phase mixing in multi-component metal-organic framework glasses constructed by quantitative elemental nano-tomography
S Collins, K MacArthur, L Longley, R Tovey, M Benning, C Schoenlieb, T Bennett, P Midgley
– APL Materials
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
Joint Motion Estimation and Source Identification using Convective Regularisation with an Application to the Analysis of Laser Nanoablations
L Lang, N Dutta, E Scarpa, B Sanson, C-B Schönlieb, J Étienne
Semi-supervised Learning with Graphs: Covariance Based Superpixels For Hyperspectral Image Classification
P Sellars, AI Aviles-Rivero, N Papadakis, D Coomes, A Faul, CB Schonlieb
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Research Groups

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




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