A new method for choosing the regularization parameter in the transmembrane potential based inverse problem of ECG

In this paper we propose an iteratively regularized Gauss-Newton method to solve the inverse ECG problem and efficiently choose the parameter of regularization. The classical stopping criterium for this regularization technique - Morozov discrepancy principle, cannot be used in our application because the noise level estimate and problem model error are typically not available. We formulate the stopping rule based on the statistical formulation of the parameter and the physiological nature of the sought solution. With Laplace operator as a regularization matrix, the regularization parameter can be seen as an indirect measure of deviation in the solution: smaller parameters lead to a broader solution range. From our knowledge about electrophysiology of the heart we can assume values of -85 mV and +25 mV as a lower and an upper estimates for transmembrane potentials. Under this assumption we stop Gaus-Newton iteration as soon as the difference between solution smallest and largest values achieves 110 mV. Three simulation protocols confirm our ansatz: the proposed method was compared with the commonly used in the feld L-curve based Tikhonov method, showing superior performance during an initial phase of an ectopic heart activation sequence.