Bayesian Optimization for the Inverse Problem in Electrocardiography

The inverse problem in electrocardiography is an ill-posed problem where the objective is to reconstruct the electrical activity of the epicardial surface of the heart, given the electrical activity on the thorax’ surface. In the forward problem, the electrical propagation from heart to thorax is modeled by the volume conductor equation with Dirichlet boundary conditions in the heart's surface, and null flux coming from the thorax. The inverse problem, however, does not have a unique solution. In order to find solutions for the inverse problem, techniques such as Tikhonov regularization are classically used, but they often deliver unrealistic solutions. As an alternative, we propose a novel approach, where a fixed solution of the volume conductor model with a source in a forward scheme is used to solve the inverse problem. The unknown values for parameters of the fixed solution can be found using optimization techniques. Due to the characteristics of the problem, where each single evaluation of the cost function is expensive, we use a specialized CMA-ES-based Bayesian optimization technique, that can deliver good results even with a reduced number of function evaluations. Experiments show that the proposed approach can deliver improved results for in-silico simulations.