Dr Martin Benning is Senior Lecturer in Inverse Problems and Machine Learning at the School of Mathematical Sciences (SMS) and Academic Member of the Digital Environment Research Institute (DERI) at Queen Mary University of London (QMUL). Prior to joining QMUL, he was a Leverhulme Trust Early Career Research Fellow, a Fellow of the Isaac Newton Trust and affiliated to the Cantab Capital Institute for the Mathematics of Information. He was awarded a PhD in applied mathematics from the University of Münster, Germany, in 2011. Prior to his current position he has worked as a postdoctoral research associate in the group of Professor Lynn F. Gladden at the Magnetic Resonance Research Centre, University of Cambridge, as a temporary associate professor in the group of Professor Jan Modersitzki at the University of Lübeck, Germany, and as a research fellow in the image analysis group of Professor Carola-Bibiane Schönlieb at the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge.
Dr Benning’s expertise is the theoretical and computational handling of inverse and ill-posed problems. In inverse problems, an unknown quantity is only accessible indirectly through the inversion of a mathematical operator. A concrete example is the recovery of an image of the interior of a human body from a set of x-ray projections taken from different angles in Computerised Tomography (CT). In nearly all relevant applications, this inversion process is highly unstable with respect to measurement errors. A remedy is the approximation of the inverses via families of continuous operators, also known as regularisation. A particular focus of his research is the fusion of model-based and data-driven regularisation approaches. As a Turing Fellow, he is interested in exploring how to develop deep neural networks with stable approximate inverses, the development of mathematical theory for these networks and their application to select problems in generative modelling.