Interview with Dr. Gaël Rigaud

February 10, 2022

Portraits in the Department of Mathematics at the University of Stuttgart.

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

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