Carola-Bibiane Schönlieb

Carola is the Head of the Cambridge Image Analysis group at the Department of Applied Mathematics and Theoretical Physics. She has been awarded the 2016 Whitehead Prize by the London Mathematical Society, a 2017 Philip Leverhulme Prize, is Director of the Cantab Capital Institute for the Mathematics of Information, Director of the EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging, and a Faculty Fellow of the Alan Turing Institute. She works on the mathematical foundations of image analysis and inverse imaging problems. She works in applied and computational mathematics with particular focus on partial differential equations, variational methods and machine learning for image analysis, including work on light microscopy and has considerable expertise in image reconstruction and inpainting.


Laboratory website

Cambridge Image Analysis (CIA) website:

Research methods


Recent publications:

M. Foged Schmidt, M. Benning, C.-B. Schönlieb, Inverse Scale Space Decomposition, to appear in Inverse Problems, arXiv:1612.09203.

L. Bungert, D. A. Coomes, M. J. Ehrhardt, J. Rasch, R. Reisenhofer, C.-B. Schönlieb, Blind Image Fusion for Hyperspectral Imaging with the Directional Total Variation, to appear in Inverse Problems, arXiv:1710.05705.

M. Burger, H. Dirks and C.-B. Schönlieb, A Variational Model for Joint Motion Estimation and Image Reconstruction, SIAM J. Imaging Sci., 11(1) (2018), 94–128. Preprint arXiv:1607.03255.

M. Burger, L. M. Kreusser, P. Markowich, C.-B. Schönlieb, Pattern formation of a nonlocal, anisotropic interaction model, Math. Models Methods Appl. Sci. 28(3) (2018), 409-451. Preprint arXiv:1610.08108.

V. Grimm, D. McLaren, R. McLachlan, C.-B. Schönlieb, R. Quispel, Discrete gradient methods for solving variational image regularisation models, Journal of Physics A: Mathematical and Theoretical 50 (29), 2017: 295201. Preprint pdf

L. Calatroni, J. C. De Los Reyes, C.-B. Schönlieb, Infimal convolution of data discrepancies for mixed noise removal, SIAM J. Imaging Sci., 10(3) (2017), 1196{1233. Preprint arXiv:1611.00690

J. Grah, J. Harrington, S. Boon Koh, J. Pike, A. Schreiner, M. Burger, C.-B. Schönlieb, S. Reichelt, Mathematical Imaging Methods for Mitosis Analysis in Live-Cell Phase Contrast Microscopy, Methods, 115, 15 February 2017, Pages 91–99. Preprint arXiv:1609.04649.

V.C. Cao, J.C. De Los Reyes, C.-B. Schönlieb, Learning optimal spatially -dependent regularization parameters in total variation image restoration, Inverse Problems 33 (7), 2017. Preprint arXiv:1603.09155

L. Calatroni, Y. van Gennip, H. Rowland, C.-B. Schönlieb, A. Flenner, Graph clustering, variational image segmentation methods and Hough transform scale detection for object measurement in images, J Math Imaging Vis (2017) 57: 269. Preprint arXiv:1602.08574

J. C. De Los Reyes, C.-B. Schönlieb, and T. Valkonen, Bilevel parameter learning for higher-order total variation regularisation models, Journal of Mathematical Imaging and Vision, 57.1 (2017), 1-25. Preprint on arXiv:1508.07243

-J. C. De Los Reyes, C.-B. Schönlieb, and T. Valkonen, The structure of optimal parameters for image restoration problems, Journal of Mathematical Analysis and Applications 434 (2016), 464-500. arXiv:1505.01953

J. Lee, X. Cai, J. Lellmann, M. Dalponte, Y. Malhi, N. Butt, M. Morecroft , C.-B. Schönlieb, and D. A. Coomes, Individual tree species classification from airborne multi-sensor imagery using robust PCA, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 9(6), p.2554 - 2567 , 2016.

L. Calatroni, C. Cao, J. C. De Los Reyes, C.-B. Schönlieb, and T. Valkonen, Bilevel approaches for learning of variational imaging models,  in: Variational Methods in Imaging and Geometric Control, Radon Series on Computational and Applied Mathematics, volume 18, 2016, 252-290. Preprint arXiv:1505.02120 

M. Burger, K. Papafitsoros, E. Papoutsellis, and C.-B. Schönlieb, Infimal convolution regularisation functionals of BV and L^p spaces, Journal of Mathematical Imaging and Vision, 55(3), 343-369, 2016. arXiv:1504.01956

J. Lellmann, K. Papafitsoros, C.-B. Schönlieb, and D. Spector, Analysis and Application of a Non-Local Hessian, SIAM Journal on Imaging Sciences, 8(4), 2161-2202, 2015. arXiv:1410.8825

M. Moeller, M. Benning, C.-B. Schönlieb, D. Cremers, Variational Depth from Focus Reconstruction, Image Processing, IEEE Transactions on, 24(12), 5369-5378. 2015. Preprint on arXiv:1408.0173

J. Lee, X. Cai, C.-B. Schönlieb, and D. Coomes, Non-parametric Image Registration of Airborne LiDAR, Hyperspectral and Photographic Imagery of Wooded Landscapes, Geoscience and Remote Sensing, IEEE Transactions on, 53(11), 6073-6084, 2015.

J. Maas, M. Rumpf, C.-B. Schönlieb, and S. Simon, A generalized model for optimal transport of images including dissipation and density modulation,  ESAIM: Mathematical Modelling and Numerical Analysis, 49(6), 1745-1769, 2015. arXiv:1504.01988

J. Lellmann, D. Lorenz, C.-B. Schönlieb, and T. Valkonen, Imaging with Kantorovich-Rubinstein discrepancy, SIAM Journal on Imaging Sciences, 7(4), 2833-2859, 2014. arXiv:1407.0221

M. Burger, J. Müller, E. Papoutsellis, and C.-B. Schönlieb, Total Variation Regularisation in Measurement and Image space for PET Reconstruction, Inverse Problems 30 (10), 105003. pdf

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, pp. 26 - 43, January 2014. pdf

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. pdf

J. C. De Los Reyes, and C.-B. Schönlieb, Image denoising: Learning noise distribution via PDE-constrained optimisation, Inverse Problems and Imaging, Vol. 7, 1183-1214, 2013. pdf

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). pdf

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. pdf

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 pdf

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. pdf

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. pdf

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. pdf. Matlab code available.

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. pdf

C.-B. Schönlieb, A. Bertozzi, Unconditionally stable schemes for higher order inpainting, Communications in Mathematical Sciences Volume 9, Issue 2, pp. 413-457 (2011), UCLA-CAM report num. 09-78 pdf

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), arXiv:0905.2404v1 [math.NA]. pdf

M. Burger, L. He, C.-B. Schönlieb, 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. pdf

M. Fornasier, C.-B. Schönlieb, 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]. pdf

J. D. Rossi, C.-B. Schönlieb, Nonlocal higher order evolution equations, Applicable Analysis. Vol. 89(6), pp. 949-960, (2010). pdf

J. Fernandez Bonder, J. D. Rossi, C.-B. Schönlieb, 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). pdf

M.Burger, S.-Y.Chu, P.Markowich, C.-B. Schönlieb, The Willmore Functional and Instabilities in the Cahn-Hilliard equation, Communications in Mathematical Sciences, Volume 6, Issue 2 (June 2008), pp. 309-329, 2008. pdf

J. Fernandez Bonder, J. D. Rossi, C.-B. Schönlieb, 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. pdf

P.Gerl, C.-B. Schönlieb and K.C.Wang, The Use of Fractal Dimension in Arts Analysis, HarFA - Harmonic and Fractal Image Analysis Journal 2004, pp. 70-73.

Lab members

Angelica I. Aviles-Rivero: Inverse problems, medical imaging, computational analysis and machine learning
Martin Benning: Singular regularisation in inverse problems
Noemie Debroux: Image registration, image segmentation
Matthias Ehrhardt: Image reconstruction in medical inverse imaging
Hanne Kekkonen: (Statistical) inverse problems, regularisation and uncertainty quantification
Yury Korolev: Inverse problems with model errors
Lukas Lang: Mathematical image analysis, variational methods and inverse problems
Jingwei Liang: Non-smooth optimisation, image processing and machine learning
Pan Liu: PDEs, calculus of variations, image processing and machine learning
Matthew Thorpe: Graphical models, optimal transport, machine learning and discrete-to-continuous limits

PhD students
Thomas Buddenkotte (co-supervision with Richard Nickl, DPMMS).
Veronica Corona (co-supervision with Stefanie Reichelt and Kevin Brindle, CRUK CI): Crossing Modalities in Cancer Imaging: Improving Diagnostics by Linking Light Microscopy with PET/MRI Using Novel Mathematical Methods.
Derek Driggs (co-supervision with Hamza Fawzi, DAMTP).
Lisa-Maria Kreusser (co-supervision with Bertram Düring and Peter A. Markowich): Mean-field equations, biological networks.
Sebastian Lunz (co-supervision with Clément Mouhot): Mathematics of deep inversion.
Simone Parisotto (co-supervision with Simon Masnou, University of Lyon): Anisotropy in image processing.
Erlend Skaldehaug Riis: Photoacoustic tomography, optimisation.
Philip Sellars (co-supervision with Anita Faul, Alistair Forbes and David Coomes): Spectral image analysis for crop classification.
Ferdia Sherry: Bilevel optimisation.
Rob Tovey (co-supervision with Paul Midgley and Rowan Leary, Material Sciences): Mathematical challenges in electron tomography.
Jonathan Williams (co-supervision with David Coomes and Tom Swinfield, Plant Sciences): Analysis of airborne imaging data.