Laplacian and Tikhonov regularization for voltage mapping with a medical device

摘要

An embodiment of a method for solving the inverse problem of electrophysiology and determining a voltage distribution on a surface of a tissue may comprise receiving a plurality of voltages collected by a plurality of electrodes adjacent to the surface, discretizing the problem using a Finite Element Method (FEM) or a Boundary Element Method (BEM), introducing one or more regularization terms to an error minimization formulation, and solving, by a processor, the voltage distribution according to the plurality of voltages and according to the regularization terms. The regularization terms may comprise one or more of a Laplacian smoothness operator, a Tikhonov regularization matrix, a confidence matrix, and a linear operator that interpolates the plurality of electrode voltages to the tissue voltage distribution.