Fetal Electrocardiogram Extraction Based on Tensor Decomposition of Multi-Dimensional Subspace Representation

Since fetal ECG (FECG) produces much lower signal amplitudes than maternal ECG (MECG), it is highly susceptible to volume-conduction effects, respiration, and fetal movements. Therefore, the observed abdominal signals exhibit pronounced nonlinear mixing and time-varying characteristics, which severely limit extraction accuracy. To tackle this complex maternal-fetal mixing, this paper pro poses a tensor decomposition of multi-dimensional sub space representation (TD-MDSC) scheme for improving ex traction accuracy and robustness. First, an adaptive multi subspace decoupling (AMSD) mechanism is developed. It employs multi-subspace mapping and hierarchical decomposition to transform the nonlinear mixtures into an approximately linear and more separable representation, thereby facilitating subsequent FECG extraction. Furthermore, a multi-domain tensorized decomposition (MDTD) strategy is developed based on tensor-decomposition theory in multidimensional signal processing. It constructs a third order covariance tensor from the second-order statistics of the observed data and their time-lagged versions to capture multidimensional statistical properties and global spatiotemporal correlations in the observed mixtures. This representation enables effective modeling and separation of the complex maternal-fetal mixtures. Experiments on four public datasets show that the proposed scheme achieves competitive performance compared with several mainstream methods in terms of fetal R-peak detection, indicating robustness under nonlinear and nonstationary mixing conditions.