What is your academic background?
My academic career may sound untypical for Germany. I first studied mathematics and physics at an "École Préparatoire" in Toulouse (France) and then moved near Paris to study electronics and biotechnology at the ENSEA engineering school. In parallel, I did a Master of Science in Image Processing at the University of Cergy-Pontoise (France). I was interested in doing a PhD in applied mathematics and image processing and at a conference I met Prof. Alfred K. Louis from Saarbrücken, Germany, who agreed to fund my PhD together with Prof. Mai K. Nguyen from Cergy-Pontoise. Thus began my history with Germany and academic research. After my PhD, I got several postdoctoral positions in Saarbrücken, Metz (France) and a lectureship in Würzburg, before I habilitated in mathematics at the University of Bremen. Since last October, I am now here at the Department of Mathematics, leading a project within the Cluster of Excellence SimTech.
What is your research about?
I am mainly concerned with the mathematics of imaging techniques. These are non-invasive techniques that can be used to study a medium, typically using electromagnetic waves that propagate and interact with the atomic structure of the object. The best-known and most established example is computed tomography (CT), which images a patient's tissue using the propagation properties of X-rays.
The exciting thing about imaging is that it connects many disciplines. The construction of a mathematical model is based on a deep understanding of the underlying physics. Many results from operator theory, functional analysis, and/or partial differential equations are used in the study of the forward model and, in particular, the associated inverse problem. The development of appropriate numerical methods is then required to obtain a stable and accurate solution. The computational cost can be very high, requiring suitable hardware and software solutions. My research therefore spans from physics to computer science with a focus on applied mathematics, especially inverse problems.
What is Compton imaging and what are the challenges that need to be overcome?
Compton imaging is a promising concept that takes advantage of the Compton scattering phenomenon and the recent development of energy-resolving scintillation crystals, which has become one of my main research interests. The Compton effect is the main interaction between X-rays or gamma rays and the atomic structure of an object illuminated by a radioactive/ionizing source. By its nature, this concept is complementary to standard imaging techniques such as computed tomography. From a mathematical perspective, Compton imaging presents some unique challenges. For example, the complexity of the forward models leads to a high degree of model uncertainty. In addition, depending on the application, there is the problem of limited data and the need to find a trade-off between measurement time and noise. This latter issue is at the heart of my project within Project Network 6 in the SimTech cluster of excellence, where we are investigating the case of moving objects such as fluids in porous media.
What constitutes academic research for you?
Freedom, imagination, inspiration. A conversation over a cup of coffee and a tablet can form the basis for important theoretical and practical results.
Thank you very much for the interview.
Dr. Gaël Rigaud
Department of Mathematics