Solving the inverse problem based on UPEMD for electrocardiographic imaging

Abstract

Current techniques used for solving the inverse problem in Electrocardiographic imaging (ECGI) to locate atrial fibrillation (AF) drivers are far from dependable and accurate. Given that body surface electrocardiographic signals (ECGs) are composed of numerous components, separation promises to be a powerful solution for the inverse operation, extracting sections with more specific components from the whole and processing them in a unique way. Therefore, this work proposes a multi-scale time–frequency domain solution based on uniform phase empirical mode decomposition (UPEMD_MSTFDS). We first utilize UPEMD to decompose the complete ECGs. Then we obtain the final solution by applying the second-order Tikhonov algorithms (Tikhonov) and truncated singular value decomposition (TSVD) to the different decomposed signal parts. To evaluate the accuracy and robustness of UPEMD_MSTFDS, two simulated datasets with or without random respiratory interference, namely baseline wander (BW), are employed. Quantitative results show that the detection accuracy of UPEMD_MSTFDS is improved by more than 10% on the first dataset including simple AF (SAF) and complex AF (CAF) when compared to popular inverse algorithms except for Bayesian maximum a posteriori estimation (Bayes). In the same condition but with BW, the weighted under-estimation indicator of UPEMD_MSTFDS drops by more than 70%, and the weighted over-estimation indicator corresponding to SAF with BW and CAF with BW drop to 39.99% and 57.03%, respectively. Moreover, both the driver and domain frequency maps computed by UPEMD_MSTFDS are most similar to the real ones of the other dataset, demonstrating that UPEMD_MSTFDS is apparently superior to existing algorithms.