At the Department of Applied Mathematics and Theoretical Physics there are several research groups working on high-level image reconstruction and processing methods as well as on imaging techniques to analyse biological processes, glaciers, and fluid flow.
The group focuses on functional analysis and harmonic analysis in applications in a broad sense. Topics of interest include: Computations in infinite dimensions, Sampling theory, Compressed Sensing, Mathematical Signal Processing, Computational Harmonic Analysis, Inverse Problems, Complexity and Computability Theory, Computational Spectral Theory, Spectral Theory and Ergodic Theory, Kinetic Theory, Multiscale Problems, Medical Imaging (MRI and CT), Seismic Tomography.
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. In particular, we are interested in: Image retrieval and enhancement from corrupted and under sampled measurements; Compressed sensing; Sparsity promoting regularisation such as total variation and higher-order regularisation; Image restoration; Image segmentation and object tracking; Large scale computing; Applications in processing of photographs, biomedical imaging (MRI, PET/SPECT, microscopy imaging), arts restoration, forensics, just to name a few.
Among other things Professor Fokas works on advanced image reconstruction methods for medical imaging, in particular PET, SPECT, EEG and MEG.
Among other things this research group develops image processing software for experimental data, aimed specifically at fluid dynamics. See DigiFlow
The group focuses on understanding nonequilibrium phenomena in the natural world, with particular emphasis on biological physics. We strive for a holistic approach in which theory and experiment seamlessly coexist, in the best tradition of DAMTP. Members of the group include theoretical and experimental physicists, chemists, applied mathematicians and biologists, and we collaborate broadly with scientists from other departments in Cambridge and beyond. Undergraduates are welcome to join us, especially for summer projects.
Image segmentation problems appear in areas such as image editing (separating foreground from background, merging multiple images), medical applications (separating gray and white matter, finding structures in medical images), and biological imaging (finding cells and nuclei, detecting cancerous cells).