Constrained Null Space Component Analysis for Semiblind Source Separation Problem

A Null Space-Based Blind Source Separation for Fetal Electrocardiogram Signals

This paper presents a new non-invasive deterministic algorithm of extracting the fetal Electrocardiogram (FECG) signal based on a new null space idempotent transformation matrix (NSITM). The mixture matrix is used to compute the ITM. Then, the fetal ECG (FECG) and maternal ECG (MECG) signals are extracted from the null space of the ITM. Next, MECG and FECG peaks detection, control logic, and adaptive comb filter are used to remove the unwanted MECG component from the raw FECG signal, thus extracting a clean FECG signal. The visual results from Daisy and Physionet real databases indicate that the proposed algorithm is effective in extracting the FECG signal, which can be compared with principal component analysis (PCA), fast independent component analysis (FastICA), and parallel linear predictor (PLP) filter algorithms. Results from Physionet synthesized ECG data show considerable improvement in extraction performances over other algorithms used in this work, considering different additive signal-to-noise ratio (SNR) increasing from 0 dB to 12 dB, and considering different fetal-to-maternal SNR increasing from -30 dB to 0 dB. The FECG detection of the NSITM is evaluated using statistical measures and results show considerable improvement in the sensitivity (SE), the accuracy (ACC), and the positive predictive value (PPV), as compared with other algorithms. The study demonstrated that the NSITM is a feasible algorithm for FECG extraction.

Eliminating the Permutation Ambiguity of Convolutive Blind Source Separation by Using Coupled Frequency Bins

Blind source separation (BSS) is a typical unsupervised learning method that extracts latent components from their observations. In the meanwhile, convolutive BSS (CBSS) is particularly challenging as the observations are the mixtures of latent components as well as their delayed versions. CBSS is usually solved in frequency domain since convolutive mixtures in time domain is just instantaneous mixtures in frequency domain, which allows to recover source frequency components independently of each frequency bin by running ordinary BSS, and then concatenate them to form the Fourier transformation of source signals. Because BSS has inherent permutation ambiguity, this category of CBSS methods suffers from a common drawback: it is very difficult to choose the frequency components belonging to a specific source as they are estimated from different frequency bins using BSS. This paper presents a tensor framework that can completely eliminate the permutation ambiguity. By combining each frequency bin with an anchor frequency bin that is chosen arbitrarily in advance, we establish a new virtual BSS model where the corresponding correlation matrices comply with a block tensor decomposition (BTD) model. The essential uniqueness of BTD and the sparse structure of coupled mixing parameters allow the estimation of the mixing matrices free of permutation ambiguity. Extensive simulation results confirmed that the proposed algorithm could achieve higher separation accuracy compared with the state-of-the-art methods.