Improve ECGI inverse problem reconstruction Introduce new mathematical approches to the field of the ECGI inverse problem Compare the performance of the new mathematical approaches to the state-of-the-art methods, mainly the MFS method used in commercial devices. In silico validation of the new approches. Assessment of some simplification hypothesis: Torso inhomogeneity Propose some uncertainty quantification apronches to deal with measurements errors Context and objectives Optimal control approach Mathematical model In silico gold standard Results Torso Heterogeneity effect Conclusions Forward model If we know the heart potential we can compute the electrical potential Inverse problem If we know the electrical potential and the current density at the outer boundary of the torso and we look for the electrical potential at the heart surface Computational heart and torso anatomical models + electrodes position Computational torso meshes: 250 nodes mesh (blue). More accurate FE mesh with 6400 nodes (green) Remarks Introducing the torso heterogeneity is natural with FEM. also anisotropy could be introduced The error is more important in the left ventricle Main results and perspectives New mathematical approches for solving the inverse problem in electrocardiography imaging based on optimal control Over all the 20 cases used in this study the optimal control method performs better than the MFS both in terms of relative error and correlation coefficient: Acknowledgment: This work was partially supported by an ANR grant part of "Investissements d'Avenir" program with reference ANR-10-IAHU-04. It is also supported by the LIRIMA international lab thought the EPICARD team