Section: New Results

Solving with games the coupled problem of conductivity or obstacle identification and data recovery

Participants : Abderrahmane Habbal, Rabeb Chamekh [PhD, LAMSIN, Univ. Tunis Al Manar] , Marwa Ouni [PhD, LAMSIN, Univ. Tunis Al Manar] , Moez Kallel [LAMSIN, Univ. Tunis Al Manar] , Nejib Zemzemi [Inria Bordeaux, EPI CARMEN] .

Based on previous successful attempts   [104], [113] to tackle ill posed inverse problems a Nash games, we consider two developments :

The first one is related to joint obstacle shape/location and data recovery. We consider a game theory approach to deal with a geometric inverse problem related to the Stokes system. The problem consists in detecting an obstacle in a flow from incomplete measurements on the boundary of a domain. The approach that we propose deals simultaneously with the reconstruction of the missing data and the identification of one or more objects immersed in a viscous and incompressible fluid flow. The solution is interpreted in terms of Stackelberg-Nash equilibrium between both problems. We develop a new obstacle detection algorithm and we consider different numerical situations to illustrate the efficiency and robustness of the method.

The second one is dedicated to the electrocardiography inverse problem. The difficulty comes from the fact that the conductivity values of the torso organs like lungs, bones, liver,...etc, are not known and could be patient dependent. Our goal is to construct a methodology allowing to solve both the data completion (heart electrical signal recovery) and conductivity identification at the same time.