Research Interests

(GIF Created by Philip Sellars)

We are interested in all aspects of mathematical imaging: the use of mathematical techniques to analyse and to improve real-world images, ranging from photographs made with consumer cameras to the images made with professional imaging devices in the sciences and medicine. These include techniques such as MRI (magnetic resonance imaging) and PET (positron emission tomography). Our current research concentrates in particular on higher order PDEs for image inpainting, and discontinuity-preserving higher-order variational approaches for the recovery of sparsely sampled data. Further themes include parameter learning, with the goal of building "black box" imaging tools suitable for use by non-professionals.

Listed below are ongoing and previous projects in alphabetical order as well as funding sources. For categorised projects, follow the links on the left.

Research Projects

Anisotropic Interaction Models for Simulating Fingerprint Patterns

Researcher: Lisa Maria Kreusser, Martin Burger, José Carrillo, Bertram Düring, Carsten Gottschlich, Stephan Huckemann, Peter Markowich, Carola-Bibiane Schönlieb

Anisotropic variational models and PDEs for inverse imaging problems

Researcher: Simone Parisotto, Carola-Bibiane Schönlieb

Cellular Mechanics of Drosophila

Researcher: Lukas F. Lang, Jocelyn Étienne, Nilankur Dutta, Bénédicte Sanson, Elena Scarpa, Carola-Bibiane Schönlieb

Faster PET Reconstruction by Stochastic Optimisation

Researcher: Matthias Ehrhardt, and Carola-Bibiane Schönlieb

Flow of Microtubules in the Drosophila Oocyte

Researcher: Lukas F. Lang, Maik Drechsler, Hendrik Dirks, Martin Burger, Carola-Bibiane Schönlieb, Isabel M. Palacios

Geometric Integration Methods for Optimisation

Researcher: Erlend Riis, and Carola-Bibiane Schönlieb

Image Classification Under Minimal Supervision: Graph-Based Semi-Supervised Learning for Real-World Large-Scale Problems.

Reseacher: Angelica Aviles-Rivero, and Carola-Bibiane Schönlieb

Inverse Problems with Imperfect Forward Models and Applications in Biomedical Imaging

Researcher: Yury Korolev, Martin Burger, Carola-Bibiane Schönlieb, Leila Muresan

Learning Sampling Patterns for MRI

Researcher: Ferdia Sherry, Erlend Riis, Luca Calatroni, and Carola-Bibiane Schönlieb

Machine learning methods for segmentation of food microscopy images

Researcher: Rihuan Ke, Carola-Bibiane Schönlieb and Peter Schuetz

Mathematical challenges in electron tomography

Researchers: Willem Diepeveen, Rob Tovey, Tatiana Bubba, M. Benning, C.-B. Schönlieb, O. Öktem, C.E. Yarman

Mathematics for Cultural Heritage Applications

Researchers: Simone Parisotto, Luca Calatroni, Rob Hocking, and Carola-Bibiane Schönlieb

Model-Based and Deep Learning-Based Approaches for Image Restoration for Real-World Problems: Image Reflection Removal and Image Deraining.

Researcher: Angelica Aviles-Rivero, and Carola-Bibiane Schönlieb

Equivariant Neural Networks for Inverse Problems

Researchers: Ferdia Sherry, Christian Etmann, Matthias Ehrhardt, Elena Celledoni, Brynjulf Owren, and Carola-Bibiane Schönlieb

Multi-sensor Remote Sensing for the Detection of Individual Trees

Researchers: Sören Dittmer, Jonathan Williams, Carola-Bibiane Schönlieb, Tom Swinfield, David A. Coomes, Juheon Lee, Xiaohao Cai

Multi-Tasking Models for Image Analysis

Researcher: Angelica Aviles Rivero, Veronica Corona, Noémie Debroux, Carola-Bibiane Schönlieb

Semi-Supervised Hyperspectral Image Classification

Researcher: Angelica Aviles Rivero, Philip Sellars, David Coomes, Nicolas Papadakis, Carola-Bibiane Schönlieb

Template-Based Image Reconstruction from Sparse Tomographic Data

Researcher: Lukas F. Lang, Sebastian Neumayer, Ozan Öktem, Carola-Bibiane Schönlieb

Tracking Tumour Dynamics

Researchers: Thomas Buddenkotte, Subhadip Mukherjee, Carola-Bibiane Schönlieb and Evis Sala

INTEGRAL: Robust and Efficient Analysis Approaches of Remote Imagery for Assessing Population and Forest Health in India

Researchers: Madeleine Kotzagiannidis, Angelica Aviles-Rivero, Rihuan Ke, Carola-Bibiane Schönlieb, David Coomes, James Woodcock, and Rahul Goel

Plug-and-Play Proximal Algorithm for Inverse Imaging Problems

Researcher: Angelica Aviles-Rivero, Jingwei Liang, and Carola-Bibiane Schönlieb

Unsupervised Learning for Image Analysis

Researcher: Angelica Aviles-Rivero, Hankui Peng, Lihao Liu, and Carola-Bibiane Schönlieb

Machine learning methods for segmentation of food microscopy images

Researcher: Rihuan Ke, Carola-Bibiane Schönlieb and Peter Schuetz

L-infinity Variational Problems

Researcher: Yury Korolev, and Carola-Bibiane Schönlieb

We study minimisers of Rayleigh quotients involving $L^\infty$ type norms such as the $W^{1,\infty}$ Sobolev norm. Notable minimisers include ground states of the $\infty$-Laplacian $\Delta_\infty$, $\infty$-harmonic functions and the distance function. We use convex analysis to characterise these minimisers and their subgradients.

Functional Analysis of Neural Networks

Researcher: Yury Korolev, and Carola-Bibiane Schönlieb

Image Reconstruction in Light Sheet Microscopy

Researcher: Yury Korolev, and Carola-Bibiane Schönlieb

Data Driven Regularisation Theory

Researcher: Yury Korolev, and Carola-Bibiane Schönlieb

Cambridge Image Analysis

Research Projects

Anisotropic Interaction Models for Simulating Fingerprint Patterns

Anisotropic variational models and PDEs for inverse imaging problems

Cellular Mechanics of Drosophila

Faster PET Reconstruction by Stochastic Optimisation

Flow of Microtubules in the Drosophila Oocyte

Geometric Integration Methods for Optimisation

Image Classification Under Minimal Supervision: Graph-Based Semi-Supervised Learning for Real-World Large-Scale Problems.

Inverse Problems with Imperfect Forward Models and Applications in Biomedical Imaging

Learning Sampling Patterns for MRI

Machine learning methods for segmentation of food microscopy images

Mathematical challenges in electron tomography

Mathematics for Cultural Heritage Applications

Model-Based and Deep Learning-Based Approaches for Image Restoration for Real-World Problems: Image Reflection Removal and Image Deraining.

Equivariant Neural Networks for Inverse Problems

Multi-sensor Remote Sensing for the Detection of Individual Trees

Multi-Tasking Models for Image Analysis

Semi-Supervised Hyperspectral Image Classification

Template-Based Image Reconstruction from Sparse Tomographic Data

Tracking Tumour Dynamics

INTEGRAL: Robust and Efficient Analysis Approaches of Remote Imagery for Assessing Population and Forest Health in India

Plug-and-Play Proximal Algorithm for Inverse Imaging Problems

Unsupervised Learning for Image Analysis

Machine learning methods for segmentation of food microscopy images

L-infinity Variational Problems

Functional Analysis of Neural Networks

Image Reconstruction in Light Sheet Microscopy

Data Driven Regularisation Theory

Study at Cambridge

About the University

Research at Cambridge