Blind source separation (BSS) has applications in the fields of data compression, feature recognition, speech, audio, and biosignal processing. Identification of ECG signal is one of the challenges in the biosignal processing. Proposed in this paper is a new method, which is the combination of related function relevance to estimated signal and negative entropy in fast independent component analysis (FastICA) as objective function, and the iterative formula is derived without any assumptions; then the independent components are found by maximizing the objective function. The improved algorithm shorthand for RFastICA is applied to extract random mixed signals and ventricular late potential (VLP) signal from normal ECG signal; simultaneously the performance of RFastICA algorithm is compared with traditional FastICA through simulation. Experimental results show that RFastICA algorithm outperforms traditional FastICA with higher similarity coefficient and separation precision.
Blind source separation (BSS) [
The detection and analysis of VLP generally appearing in the end of QRS wave and extending to ST segment with a series of high frequency and lowrising weak irregular electrical signal are a kind of effective means to predict unexplained asphyxia, sudden cardiac deaths, and so forth [
To overcome the abovementioned limitation and improve the detection accuracy, it is necessary to put forward a new detection technology. Independent component analysis (ICA) as a branch of BSS is widely applied to this problem in recent years [
RFastICA is proposed in this paper, which is the combination of related function and negative entropy as objective function, and the iterative formula is derived; then the independent components are found by maximizing the objective function. The extracted performance of RFastICA algorithm is compared with traditional FastICA through simulation of random mixed signals and ECG signal with VLP. Experimental results show that RFastICA algorithm outperforms traditional FastICA with higher similarity coefficient and separation precision.
ICA firstly proposed by Pierre Comon in 1994 is a method for finding the statistical independent components from multidimensional statistical data [
The goal is to extract independent source signals from mixed signals by finding separation matrix
Generally, the normal ECG and VLP signal can be thought of as statistical independence with each other; thus VLP signal will be extracted through FastICA algorithm [
The basic model is shown in Figure
FastICA principle diagram.
Traditional FastICA method is to estimate source signals based on negative entropy.
In order to improve separation precisely, negative entropy combined with related function as objective function is proposed in this paper. The updating formula of RFastICA algorithm is vector gradient derived by the negative entropy combined with related function. The basic idea of RFastICA algorithm requires that extracted signals are not only independent but also have high precision. Related function
The MSE in type (
Source signal is replaced by the average of estimated signal. It is defined by
BSS model is
Combining type (
From the above,
Vector gradient is defined as
The gradient of
Type (
In literature [
The objective function is composed by negative entropy and related function including the information between source signal and estimated signal in RFastICA:
The vector gradient of objective function
Type (
A familiar measure of separation performance is the similarity coefficient defined as [
When
The composite scattering plot [
In order to indicate the performance of RFastICA compared with traditional FastICA, the following simulations were conducted.
Taking random signals as an example in the first simulation, RFastICA method was proved to be effective. In the second simulation, taking ECG signal with VLP as an example, the original ECG signal without noises was from MIT/BIH database and VLP signal was generated through stacking sine waves with different frequency and amplitude [
In this simulation, the source signal
The source signals.
The mixed signals.
The mixed signals were extracted through RFastICA and traditional FastICA in Figures
Extracted signals with RFastICA.
Extracted signals with traditional FastICA.
In the experiment of extracting random signals, the comparison of similarity coefficient matrix between RFastICA and FastICA algorithm was shown in Table
The comparison of similarity coefficient matrix.
RFastICA  FastICA  

Similarity coefficient matrix 


Extracted signal
The composite scattering plot with RFastICA algorithm.
The composite scattering plot with FastICA algorithm.
From the above experiments, we could see that RFastICA algorithm outperforms traditional FastICA with higher similarity coefficient and separation precision.
In this simulation, the source signal
The source signals.
The observed signals.
The mixed signals were extracted through RFastICA and traditional FastICA in Figures
Extracted signals with RFastICA.
Extracted signals with FastICA.
In the experiment of extracting VLP signal, the comparison of similarity coefficient matrix between RFastICA and FastICA algorithm was shown in Table
The comparison of similarity coefficient matrix.
RFastICA  FastICA  

Similarity coefficient matrix 


Extracted signal
The composite scattering plot with RFastICA.
The composite scattering plot with FastICA.
From the above experiments, the performance of RFastICA is superior to the FastICA obviously with higher similarity coefficient and high separation precision.
In this paper, RFastICA algorithm and FastICA algorithm were adapted to extract random signals and to separate VLP signal from ECG signal. We believed that our study produced two important results. Firstly, we proposed a new method through the combination of related function and negative entropy and separated independent components by maximizing new objective function in the experiments. On the other hand, the experiments showed that RFastICA method outperformed traditional FastICA method with higher similarity coefficient and high separation precision.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This project is supported by The General Object of National Natural Science Foundation (no. 61371062), Youth Science Foundation Project of National Natural Science Foundation (no. 61303207), Ministry of Education in 2012 Colleges and Universities by the Specialized Research Fund for the Doctoral Program of Joint Funding Subject (no. 20121402120020), Shanxi Province Science and Technology Development Project, Industrial Parts (no. 2012032102401), Shanxi International Science and Technology Cooperation Project (no. 2012081031), Science and Technology Activities Project of Study Abroad Returnees in Shanxi Province in 2012 (Funded by Shanxi province human resources and social security hall), and Research Project supported by Shanxi scholarship council of China (no. 2013032).