Two-Step Tikhonov method for solving ECGI inverse problem

Background Electrocardiographic Imaging (ECGI) is a non-invasive technology that reconstructs cardiac electrical activity from body-surface electrocardiograms. Its implementation has two steps: forward model construction and inverse problem solving. The existing methods for solving inverse problems typically assume that the forward problem has been accurately solved, ignoring the associated uncertainties. Objective This study aims to integrate forward numerical methods with inverse regularization algorithms to enhance ECGI inverse solution accuracy. Methods The Two-Step Tikhonov (2S-Tik) method combines the forward numerical and inverse regularization methods, employing the inverse-derived regularization parameter to refine the transfer matrix. First, the optimal regularization parameter λ opt is identified via the L-curve method in the 0th-order Tikhonov algorithm. Then, λ opt is fixed, and the optimal A opt is sought within the search space of the transfer matrix A. Finally, the selected λ opt and A opt are combined for solution. Results For sinus rhythm, the spatial (sCC) and temporal (tCC) correlation coefficients of cardiac surface reconstructed electrical potentials using the 2S-Tik method are approximately 0.72 ± 0.21 and 0.90 ± 0.19, respectively, improving sCC and tCC by 10% and 6% over the traditional Tikhonov algorithm (0.65 ± 0.26 and 0.85 ± 0.21). Moreover, when Gaussian noise is added to body-surface potentials, the 2S-Tik method exhibits robust and stable performance. Conclusion Compared with the traditional Tikhonov algorithm, the 2S-Tik method significantly improves the accuracy of ECGI inverse solution and has great potential in clinical ECGI applications.