Analytical models combined with data-driven techniques in dynamic Compton scattering tomography

The purpose of the project is to develop suited data-driven and learning techniques enhanced by the analysis of a given inverse problem. The application of interest is the so-called Compton scattering tomography which is a novel imaging technique which, in contrast with conventional CT (computerized tomography), exploits the energy as a new imaging parameter delivered by recent scintillators. A new issue tackled by this project is to consider time-dependent objects, for instance liquids in porous media. The project does not limitate to this sole application and strives to develop a general framework. The project explores three paths which are complementary:

1. We propose first to deal with the problem of  motion and noise using a stochastic view. While giving good results, the method tends to be too smooth. This is the reason why we are developing an algorithm based on neural networks which overcomes this limitation by introducing learned edge-preserving regularizers in the stochastic approach.
2. We also need to answer the problem of limitations in the data which leads to artifacts and unreconstructed area. These limitations in imaging can be interpreted and quantified by microlocal analysis. We propose to combine standard learned primal-dual algorithms by microlocal analysis and enhanced by feature extraction. The overall networks will then perform an “impainted” reconstruction driven by microlocal analysis.
3. Finally, we are experimenting on a specific architecture based on the Deep Image prior in order to solve the auxiliary problem associated to an inverse problem. The goal is to learn a reconstruction kernel of a (linear) operator which could be applied then on corrupted and limited data.