Computational Intelligence and Neuroscience

Volume 2019, Article ID 8432953, 10 pages

https://doi.org/10.1155/2019/8432953

## Wavelet-Based Semblance Methods to Enhance the Single-Trial Detection of Event-Related Potentials for a BCI Spelling System

^{1}Escuela de Ingeniería C. Biomédica, Universidad de Valparaíso, Valparaíso, Chile^{2}Université de Lorraine, CNRS, INRIA, LORIA, F-54000 Nancy, France^{3}Centro de Investigación y Desarrollo en Ingeniería en Salud, CINGS, Universidad de Valparaíso, Valparaíso, Chile

Correspondence should be addressed to Carolina Saavedra; lc.vu@ardevaas.anilorac

Received 4 January 2019; Revised 8 April 2019; Accepted 18 May 2019; Published 26 August 2019

Academic Editor: Laura Marzetti

Copyright © 2019 Carolina Saavedra 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

Based on similarity measures in the wavelet domain under a multichannel EEG setting, two new methods are developed for single-trial event-related potential (ERP) detection. The first method, named “multichannel EEG thresholding by similarity” (METS), simultaneously denoises all of the information recorded by the channels. The second approach, named “semblance-based ERP window selection” (SEWS), presents two versions to automatically localize the ERP in time for each subject to reduce the time window to be analysed by removing useless features. We empirically show that when these methods are used independently, they are suitable for ERP denoising and feature extraction. Meanwhile, the combination of both methods obtains better results compared to using them independently. The denoising algorithm was compared with classic thresholding methods based on wavelets and was found to obtain better results, which shows its suitability for ERP processing. The combination of the two algorithms for denoising the signals and selecting the time window has been compared to xDAWN, which is an efficient algorithm to enhance ERPs. We conclude that our wavelet-based semblance method performs better than xDAWN for single-trial detection in the presence of artifacts or noise.

#### 1. Introduction

Brain-computer interface (BCI) research endeavours to provide new ways of communication for severely handicapped people by translating their brain activity into commands that can be used in a computer or other devices, without using the standard peripheral nerves and muscular pathways. In particular, brain-computer interfaces are control and communication systems that are designed to assist people with motor disabilities, such as people suffering from amyotrophic lateral sclerosis (ALS), spinal cord injury, multiple sclerosis, muscular dystrophies, and cerebral palsy. In this paper, we will focus on the noninvasive BCI [1].

Electroencephalography (EEG) is a noninvasive way of measuring over the scalp the electrical activity occurring as the product of the interactions of neurons in the brain [2]. EEG recordings are usually overlapped with noise and artifacts such as muscle activity. Their presence hinders EEG detection and requires novel methods to remove them from the underlying true brain signal. One important assumption about noise is that it is supposed to be independent of brain activity. It is assumed that brain signals are (almost) instantaneously recorded by the electrodes, implying that each recorded channel is highly correlated with the others. Accordingly, it is possible to conclude those signal components that are not correlated over channels are assumed to be noise or artifacts and can be removed from the recorded signals. A comprehensive survey of signal-processing algorithms for EEG applied to the BCI can be found in [3].

Event-related potentials (ERPs) are neural activities generated involuntarily as a consequence of the occurrence of an expected but rare event. A deflection appears in the EEG signal with a specific polarization and latency. For example, P300 is a cognitive ERP with a positive peak at 300 ms after the stimulus. ERP can potentially be detected with signal-processing techniques and used as a control command in BCI applications, such as the very well-known P300 speller proposed by Farwell and Donchin [4].

Unfortunately, major obstacles still exist in the use of EEG for brain-computer interfaces: signal changes to be detected are very small and high noise such as the signal depletion due to the skull or muscular artifacts is present. To enhance and detect the ERP response, it is necessary to repeat the stimuli and average the responses; however, this reduces the information transfer rate. Several efforts to reduce the number of averaged trials or to directly perform single-trial ERP detection have been made [5–8]. The intention of improving the single-trial classification performance ranges from increasing the database, adding artificial trials [9], where original data are deformed to create new artificial patterns, to EEG source reconstruction or transfer learning methods, where data from multiple users are used to train classifiers to improve the BCI system [10, 11]. The single-trial approach saves time, but the signal-to-noise ratio (SNR) is very low, making ERP detection difficult. On the contrary, when the stimuli are repeated to enhance the ERP detection, these repetitions may become tedious and tiring for the user, and the averaging technique decreases the speed of the spelling. Another problem related to the average of repetitions is the assumption of stationarity. Latency jitter, amplitude variability, or phase artifacts between single trials can cause a flattening up to the elimination of transient characteristics [12, 13].

Usually, in P300-based BCI systems, a temporal window is manually selected [14]. This window is usually chosen to be large enough (within a range of [0, 1] second) to ensure including the ERP components under the study, independently of the user reaction time to the stimulus. However, the ERP responses have different latencies (and amplitudes) for each subject, which comprise irrelevant data to be covered in the temporal window. This can increase both the difficulty of training a classifier with irrelevant variables and the complexity of detecting the ERP. The variance among trials can provide information on the subject’s cognitive state, allowing comparisons to be made between subjects [15].

Several studies have shown that it is possible, yet difficult, to distinguish single-trial signals from the EEG background [16–18]. A popular technique is the xDAWN algorithm [19] which automatically enhances the ERP for classification by using spatial filters, combining the multichannel information to put aside useless components. An exhaustive comparative study of several classification techniques is given in [20]. A review of state-of-the-art methods for single-trial detection of event-related potentials can be found in [21]. Finally, a complete survey of the issues that should be considered when designing a new P300-based BCI paradigm can be found in [22].

Wavelets theory has been used in several studies for P300 detection [23–25]. In particular, some advances using wavelets for single-trial detection can be found in [16, 26], where automatic denoising methods are recommended. The fundamental hypothesis of wavelet denoising is that large coefficients correspond to the signal and small coefficients correspond to the noise [27]. The problem with current methods is that they can only denoise one channel at a time, regardless of the information on other channels. This causes them to lose the information provided by the ensemble, such as phase and amplitude information. In ERP studies, the most common mother wavelets that are used are the quadratic B-spline [28–30], the Daubechies wavelets Db4 and Db8 [31], the Symlet wavelet [31, 32], and Coiflet [33]. For example, in [34], a single-trial P300 detection algorithm is presented based on independent component analysis (ICA) and wavelets. Nevertheless, despite these advances, single-trial P300 detection still needs to be improved before it can be made more available for the general public.

In this paper, we introduce a novel method to denoise, localize, and isolate ERPs combining two approaches based on wavelet theory. This formalism is used to study single-trial brain signals based on similarity measures. The first approach simultaneously denoises the signals by using the phase information provided by all the channels in a single trial. Afterward, the second approach combines the phase and the amplitude information of the signals to optimize the time window of the ERP for each user.

The rest of this paper is organized as follows: In Section 2, we presented wavelet theory and semblance analysis to introduce our proposal of using the correlated information of recorded channels to remove noise and automatically establish an appropriate time window for the analysis of each subject. The results are provided in Section 3 and the discussion in Section 4. Finally, our conclusions are given in Section 5.

#### 2. Materials and Methods

##### 2.1. Wavelet Transforms

The wavelet transform is the inner product of a signal with scaled and shifted versions of a *mother wavelet * function [35]. The *continuous wavelet transform* (CWT) uses a continuous wavelet function for the signal analysis:where and change continuously and is the complex conjugate of . The CWT coefficients measure the variation of in a neighborhood of point , whose size is proportional to , obtaining a mapping of a one-dimensional signal into a two-dimensional space.

On the contrary, the *discrete wavelet transform* (DWT) uses filter banks to obtain a multiresolution time-frequency representation. More precisely, the discrete orthogonal wavelet decomposition is obtained using a discretised scale and translation.

##### 2.2. Semblance Analysis

Wavelet analysis is also useful for bivariate analysis, making it possible to study two different signals to discover the relationship between them. Cross-wavelet analysis allows us to find the mutual characteristics between signals using the available information in the wavelet transform. The cross-wavelet spectrum [36] of two different signals and is defined by their wavelet decompositions and as follows:where is a complex value and can be decomposed into amplitude and phase .

*Semblance analysis* [37] was introduced to compare two given signals and based on the phase correlations between their wavelet decompositions and using *θ*:where is an odd integer that is greater than zero. The reason why should be odd is to preserve the sign of the cosine. The use of large numbers for also produces a sharp semblance response, as demonstrated in [37].

The values of correspond to the phase correlation between the two signals, where means they are fully correlated, means they are fully inversely correlated, and means they are not correlated. Also, it is possible to analyse the signal’s amplitudes combining the phase information with the amplitude information as follows:

##### 2.3. Multisemblance Analysis

The semblance concept was extended to compare more than two signals at the same time. This measure is called the *mean resultant length* (MRL), and it was presented by Cooper in [38] based on circular statistics [39]. The MRL can be calculated according to the number *N* of signals treated, at each scale *a* and time *t*:

For more than two signals, the inversely correlated concept does not apply. This is verified by the MRL values ranging from 0 for uncorrelated signals to 1 for correlated signals.

##### 2.4. Denoising Based on the Similarity in the Channels

We propose to denoise EEG signals considering the information of all channels based on their phase and correlations within the DWT transform. Let **X** be the matrix containing the whole dataset, and let be the signal recorded by the electrode, , at time *t*, . The matrix of the recorded EEG signals can be defined as . The denoising, through thresholding, can be done using the MRL coefficients, i.e., using coefficients obtained for all channels (equation (6)), instead of the individual channel coefficients. We prune all the coefficients that are below a given threshold to zero in order to reconstruct the signal using the filtered wavelet coefficients. The MRL computation is done through the combination of the phase angles of the real and imaginary parts of the wavelet decomposition. DWT uses wavelet families that are orthogonal to each other so that the imaginary part can be achieved by the Hilbert transform of the channel [38].

In simple words, we keep those components with high similarity between channels to produce a denoised EEG signal. This novel approach is called *multichannel EEG thresholding by similarity* (METS), and the full wavelet denoising process is described in Algorithm 1.