Regularization of the inverse problem in electrocardiography: A model study

An analytic, eccentric-spheres model was used to test the efficacy of different regularization techniques based on the Tikhonov family of regularizers. The model, although simple, retains the relative size and position of the heart within the body and may incorporate all the inhomogeneities of the human torso. The boundary-element method was used to construct a transfer matrix relating the body surface potentials to the epicardial potentials, for the homogeneous form of the model. Different regularization techniques were compared in the presence of surface potential noise and in the presence of errors in estimating the conductivities, the heart size and the heart position. Results indicate that the relative error in the inverse-recovered epicardial potential with regularization does not rise proportionally to the noise level. The relative error (RE) with a 5% Gaussian noise level is 0.17; with 20% it is 0.29. Additionally, the regularized inverse procedure is shown to restore smoothness and accuracy to the inverse-recovered epicardial potentials in the presence of errors in estimating the heart position and heart size, which, using an unregularized inversion, would lead to large-amplitude oscillations in the solution.