Computational and Mathematical Methods in Medicine

Volume 2018, Article ID 1482874, 9 pages

https://doi.org/10.1155/2018/1482874

## Common Interferences Removal from Dense Multichannel EEG Using Independent Component Decomposition

School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China

Correspondence should be addressed to Xiaolin Huang; nc.ude.ujn@gnauhlx and Yun Ge; nc.ude.ujn@nuyeg

Received 26 October 2017; Revised 14 February 2018; Accepted 18 March 2018; Published 27 May 2018

Academic Editor: Fei Chen

Copyright © 2018 Weifeng Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

To improve the spatial resolution, dense multichannel electroencephalogram with more than 32 leads has gained more and more applications. However, strong common interference will not only conceal the weak components generated from the specific isolated neural source, but also lead to severe spurious correlation between different brain regions, which results in great distortion on brain connectivity or brain network analysis. Starting from the fast independent component analysis algorithm, we first derive the mixing matrix of independent source components based on the baseline signals prior to tasks. Then, we identify the common interferences as those components whose mixing vectors span the minimum angles with respect to the unitary vector. By assuming that both the common interferences and their corresponding mixing vectors stay consistent during the entire experiment, we apply the demixing and mixing matrix to the task signals and remove the inferred common interferences. Subsequently, we validate the method using simulation. Finally, the index of global coherence is calculated for validation. It turns out that the proposed method can successfully remove the common interferences so that the prominent coherence of mu rhythms in motor imagery tasks is unmasked. The proposed method can gain wide applications because it reveals the true correlation between the local sources in spite of the low signal-to-noise ratio.

#### 1. Introduction

Electroencephalogram (EEG) collected from the scalp is the integration of the electrical activities of amounts of cortex neurons blurred by the skull [1]. Although it is widely accepted that EEG has the advantage of high temporal resolution, the spatial resolution remains as a problem [2]. To improve the spatial resolution, dense multichannel EEG (with more than 32 channels) and high-density EEG (with more than 128 channels) have gained more and more applications. However, the more the channels are used, the more the redundant information is involved. It directly results in the fact that the weak components generated from the specific isolated neural source are deeply concealed by the common components from the surrounding sources [3]. Moreover, these redundancies can lead to a spurious correlation/coordination between different brain regions while in fact little or none is present. It will greatly distort the result of the brain connectivity or brain network analysis, which becomes more and more popular [4–15]. Therefore, it is of great importance to unmask the isolated source-corresponding component from the originally collected signals with too much redundant information or common interferences.

Among multichannel EEG redundancy-removal methods, one representative is surface Laplacian reference scheme [16, 17]. After subtracting the average potential in the local neighborhood, the original signals referencing to one or two common locations are converted to referencing to the respective local one. Typically, the signal amplitude will greatly decrease, with the expected return of redundancy removal. The surface Laplacian reference scheme is theoretically simple and easy to implement. However, using the arithmetical mean within the neighborhood as the local reference may be a little bit rough, regardless of the conduction differences among the neighbor leads. In addition, great attention should be paid to the selection of the neighborhood.

Another representative is independent component analysis (ICA) [18, 19]. In fact, ICA has long been applied to EEG preprocessing [20–27] including electrooculography artifacts removal. Recently, Whitmore and Lin have succeeded in removing distal electrical reference as well as volume-conducted noises from local field potentials using ICA [25]. It greatly motivates us to step further, trying a more general common interference removal.

In the presented manuscript, we do not identify the source or the frequency of the common interference. Instead, we only assume that the common interference will affect the different channel most evenly and the mixing vectors keep constant during the whole experiment, regardless of the mental activities. In addition, by regarding both the common interferences and their transfer vectors as identical in the entire experimental circumstance, we adopt the component extracted from the baseline data. We validate the proposed method on BCI competition dataset 1 [28, 29]. It turns out that the method can successfully unmask the coherence in mu rhythm during a motor imaginary task. Since high-density EEG and brain connectivity or brain network are the trends in neuroscience, the proposed method can gain wide applications.

In the manuscript, we first describe the method in Section 2, and then in Section 3 the method is validated using simulation series as well as experimental data provided in BCI Competition IV, and finally results are discussed in Section 4.

#### 2. Methods

The method includes three steps in order: independent components decomposition, the common interference identification, and removal and inverse transformation.

##### 2.1. Independent Component Decomposition

Mathematically, given the independent sources as , in which represents the sampling time index, the* N*-channel () collected signal denoted as , can be calculated as in which is the* N*-by-*M* mixing matrix. Theoretically, each row of represents a set of combination weights of the different sources on the specific channel, and each column of , denoted as , reflects the relative impacts of the* j*th source on all the different channels.

The independent component decomposition is to resolve (1) to obtainwhere is called demixing matrix. Because neither nor is known a priori, the maximization of non-Gaussianity or minimization of mutual information principle is conventionally employed to approximate the as well as through iteration [12].

Herein, we adopt FastICA algorithm proposed by Hyvärinen [13] for independent component decomposition. The fixed-point iteration scheme as well as the maximum-negative entropy principle is employed to find the orthogonal rotation matrix with the maximal non-Gaussian measure of the prewhitened data. And then the mixing matrix can be calculated as

##### 2.2. Common Interference Identification and Removal

Subsequently, we try to identify and remove the common interference through analyzing the mixing matrix .

The putative common interference component is assumed as a distal signal that has approximately same effect on all electrodes. In order to obtain local brain activities more accurately, these distal common interference components should be removed. To do this, the vector angles are calculated between each and a unit vector, and the smaller the angle is, the more uniform the impacts of the corresponding source (independent component) across channels are and the more likely the corresponding source is a common interference. We delete this source through setting the corresponding* k*th independent source as 0, obtain the processed , and finally derive the deabundancy signals as

#### 3. Experiments

##### 3.1. Simulation

To validate the proposed method, we first applied it to simulation series. We define the three collected channel signals which are determined by three independent components, i.e., , , and random Gaussian noises with , , and the mixing matrix . As described in Section 2, the collected signals are derived by . The Gaussian component is deliberately set with great amplitude and is treated as the common interference. Theoretically, we can obtain the pure signal without common interference via setting the 3rd column elements as 0 s. We plot the pure signal of Channels 1 and 2 in Figure 1(a), and the collected contaminated signals in Figure 1(b). Then, we apply the proposed method to . After common interference removal, signals of Channels 1 and 2 are plotted in Figure 1(c). To quantitatively evaluate the signal quality, we also calculate the linear correlation coefficient between the collected signals and the pure signals, both before and after common interference removal.