Robustness of the blind source separation with reference against uncertainties of the reference signals.

The fetal electrocardiogram (ECG) could provide clinical information concerning physiological conditions of the fetus. In order to extract fetal ECG, we proposed the novel algorithm, the blind source separation with reference (BSSR), which successfully extracts a complete waveform of QRS complex and avoids uncertainty in the order of the extracted signals. In the BSSR, the reference signal is supposed to be generated from the ultrasonic Doppler signal. Thus generated reference is expected to suffer from uncertainties in waveform and occurrence timing. Based on simulations, the BSSR is shown to have robustness against the uncertainties of reference signals. In addition, it is shown how the robustness depends on the order of power of correlation function between the reference and extracted signals, which composes a performance function of the BSSR.

A novel extraction method of fetal electrocardiogram from the composite abdominal signal.

In contrast to the ultrasonic measurement of fetal heart motion, the fetal electrocardiogram (ECG) provides clinically significant information concerning the electrophysiological state of a fetus. In this paper, a novel method for extracting the fetal ECG from abdominal composite signals is proposed. This method consists of the cancellation of the mother's ECG and blind source separation with the reference signal (BSSR). The cancellation of the mother's ECG component was performed by subtracting the linear combination of mutually orthogonal projections of the heart vector. The BSSR is a fixed-point algorithm, the Lagrange function of which includes the higher order cross-correlation between the extracted signal and the reference signal as the cost term rather than a constraint. This realizes the convexity of the Lagrange function in a simple form, which guarantees the convergence of the algorithm. By practical application, the proposed method has been shown to be able to extract the P and T waves in addition to the R wave. The reliability and accuracy of the proposed method was confirmed by comparing the extracted signals with the directly recorded ECG at the second stage of labor. The gestational age-dependency of the physiological parameters of the extracted fetal ECG also coincided well with that of the magnetocardiogram, which proves the clinical applicability of the proposed method.

Measurement method for the fetal electrocardiogram.

A fetal electrocardiogram (ECG) provides clinically significant information concerning the electrophysiological states of a fetus. Since the first attempt by Cremer in 1906, for about 100 years nobody has been able to non-invasively extract the fetal ECG popularly used in clinical situations. The low amplitude of the fetal signals and the high background noise and the non-linearity of the ECG signals mainly have been interfering with the noninvasive extraction of the fetal ECG. The aim of this paper is to introduce a new nonlinear filtering method to extract the fetal electrocardiogram detected from the mother's abdominal wall. This method consists of two steps: The rough extraction step performed by blind source separation (BSS) with references and the precise extraction step with fast non-linear state space projection (FNSSP) based on a nonlinear state space projection (NSSP), which needs several complicated conditions or has limitations. So, it takes a lot of time to calculate. Our new method does not require such conditions, and it has about a thirty-fold speedup when compared with the previous method. Our new method has been successfully applied to on-line recordings with fetal components and will be useful for monitoring the fetal electrocardiogram in clinical applications.