Inverse Problems typically involve the recovery of some physical characteristics of a material from its response to some excitation such as electromagnetic fields, heat, or mechanical vibrations. Inverse problems are often illposed, which means the process of recovering the unknown parameters is very sensitive to errors in the measured response. The group looks at both practical and theoretical aspects of the subject, working closely with engineers and scientists in industrial and medical research, as well as other mathematicians.
Some of the applications of inverse problems in which they are interested: Medical imaging using electricity (EIT), for example to reduce ventilator related lung injury Medical optical tomography; Industrial process monitoring using electrical measurement; Photoelasticity - visualisation of the stress inside a transparent object; Geophysical imaging; Electromagnetic monitoring of molten metal flow; Airport X-ray scanners; X-ray tomography in material science; Next generation metal detectors for security screening and land mine detection.
William is Professor of Applied Mathematics and specialises in Inverse Problems. He is interested in theory, especially inverse boundary value problems for PDEs and integral geometry (such as tensor tomography problems). Practically, he is interested in biomedical and industrial applications of electrical impedance tomography, X-ray CT for airport security, photoelastic tomography, advanced metal detectors and magnetic induction tomography, ansiotropic inverse problems for Maxwell's equations.
Oliver is a Lecturer of Applied Mathematics at the University. His research interests include Applied Mathematics, Scientific Computing, with a special interest in inverse problems, physics based imaging and numerical optimization. He is currently working on the following projects: Inverse problems for the radiative transfer equation and Microwave medical imaging and ground penetrating radar.
Sean is also a Lecturer of Applied Mathematics at the University. His research interests include inverse problems, PDES, and differential geometry. One of the main themes of his past and ongoing research has been the application of methods from microlocal analysis to questions of stable invertibility for a variety of inverse problems in tomography and seismic imaging. A general heuristic for inverse problems is that stable inversion is possible if the singularities of the quantity to be reconstructed appear in the data, and he is interested in investigating applications of this general principle