A convex relaxation framework for initialization of activation-based inverse electrocardiography

In inverse electrocardiography (ECG), the problem of finding activation times on the heart noninvasively from body surface potentials is typically formulated as a nonlinear least squares optimization problem. Current solutions rely on iterative algorithms which are sensitive to the presence of local minima. As a result, improved initialization approaches for this problem have been of considerable interest. In this work, we establish a mathematical optimization framework for the inverse problem, formally show that it is non-convex, and construct a convex relaxation whose solution we use to initialize an iterative algorithm for the original problem. We use simulated experiments based on real canine heart data to test and evaluate this method.