DROITE: Dynamic ROI tomography, Theory and Experiments

DROITE is the ANR project ANR-12-BS01-0018.

DROITE is a fundamental research project. Computed tomography aims at reconstructing images of internal physical quantities (attenuation coefficients, radioactivity concentrations) from external measurements (X-ray projections, radiation detectors). To first order, these measurements can be mathematically modeled by the Radon transform: straight line integrals of the unknown function. The problem to solve is the reconstruction of a function from a set of line integrals. Solving this problem led to the development of CT medical scanners, PET and SPECT. However, open questions remain that restrict the use of such systems in certain circumstances:

• In case of patient movement during the data acquisition, solving the inverse problem (even when the exact movement is known) is an open problem, except for some very particular motion classes.
• The use of a relatively small detector compared to the patient size, and the need to minimize the X-ray dose to the patient, lead to the problem of reconstruction from truncated projections. This is a challenging open problem that will be addressed in the project. Over the past decade, much progress has been made on reconstruction from truncated data, but open questions still remain related to the interior problem. The interior problem is well known to have no unique solution, but the uniqueness question for the reconstruction of an interior region from truncated projections when some supplementary non-truncated projections are available, remains an open problem.
• Finally, the third open question which we will attack is the combination of patient motion with truncated projections, for which virtually no results exist today.

The objective of DROITE is to make theoretical contributions to the field of dynamic CT (reconstruction of moving objects) and Regions Of Interest (ROI) reconstruction (reconstruction from truncated projections). The objectives are to solve mathematical problems arising from the open questions presented above (obtaining results on existence, uniqueness, and stability for dynamic ROI reconstruction), to develop the associated reconstruction algorithms, and to experimentally validate the results using simulated and real data.

DROITE is a project with strong interaction between mathematics and medical imaging. The mathematical problems under investigation are motivated by image-guided therapy at Centre Léon Bérard (CLB, Lyon) and the Centre d'Investigation Clinique - Innovation Technologique (CIC-IT, Grenoble University Hospital). Thus, the DROITE consortium brings together on one hand, research teams in the mathematics of tomography (TIMC-IMAG: Laurent Desbat, LHC: Rolf Clackdoyle, Catherine Mennessier), and on the other hand physicians and medical imaging experts (for image-guided radiotherapy: Myriam Ayadi, Simon Rit and David Sarrut at CLB/CREATIS; for image guided orthopeadic surgery: Ivan Bricault, Philippe Cinquin, Alexandre Moreau Gaudry at CIC-IT/TIMC-IMAG). They will participate on the experimental validation using medical data.

Therefore, the DROITE project addresses two priorities of the SNRI: numerical sciences society, with the mathematical analysis; and simulation of imaging systems in the context of medical applications and health care.