Extract fetal ECG from single-lead abdominal ECG by de-shape short time Fourier transform and nonlocal median

The multiple fundamental frequency detection problem and the source separation problem from a single-channel signal containing multiple oscillatory components and a nonstationary noise are both challenging tasks. To extract the fetal electrocardiogram (ECG) from a single-lead maternal abdominal ECG, we face both challenges. In this paper, we propose a novel method to extract the fetal ECG signal from the single channel maternal abdominal ECG signal, without any additional measurement. The algorithm is composed of three main ingredients. First, the maternal and fetal heart rates are estimated by the de-shape short time Fourier transform, which is a recently proposed nonlinear time-frequency analysis technique; second, the beat tracking technique is applied to accurately obtain the maternal and fetal R peaks; third, the maternal and fetal ECG waveforms are established by the nonlocal median. The algorithm is evaluated on a simulated fetal ECG signal database ({\em fecgsyn} database), and tested on two real databases with the annotation provided by experts ({\em adfecgdb} database and {\em CinC2013} database). In general, the algorithm could be applied to solve other detection and source separation problems, and reconstruct the time-varying wave-shape function of each oscillatory component.