Dr. Weihong Guo won the Innovation Week’s invention award for her patent with a former PhD student Richard Lartey (now at Cleveland Clinic Foundation) and Medtronic Distinguished Scientist and Technical Fellow Qingguo Zeng. The patent is entitled Graph Total Variation for ECGI. Systems and methods for graph total variation (GTV) based reconstruction of electrical potentials on a cardiac surface are disclosed. GTV-based systems and methods incorporate information about the graph structure of the heart surface as well as imposing sparsity constraints on neighboring nodes. To this end, the present disclosure uses a novel way of calculating derivatives on irregular meshes, and provides a fast solver to compute an inverse solution more efficiently than in previous systems and methods. Moreover, fast-changing signals can be recovered with less smoothing and thus greater fidelity to the original signals.