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A Brain-Computer Interface (BCI) is a system used to communicate with an external world through the brain activity. The brain activity is measured by electroencephalography (EEG) signal and then processed by a BCI system. EEG source reconstruction could be a way to improve the accuracy of EEG classification in EEG based brain-computer interface (BCI). The source localization of the human brain activities can be an important resource for the recognition of the cognitive state, medical disorders, and a better understanding of the brain in general. In this study, we have compared 51 mother wavelets taken from 7 different wavelet families, which are applied to a Stationary Wavelet Transform (SWT) decomposition of an EEG signal. This process includes Haar, Symlets, Daubechies, Coiflets, Discrete Meyer, Biorthogonal, and reverse Biorthogonal wavelet families in extracting five different brainwave subbands for source localization. For this process, we used the Independent Component Analysis (ICA) for feature extraction followed by the Boundary Element Model (BEM) and the Equivalent Current Dipole (ECD) for the forward and inverse problem solutions. The evaluation results in investigating the optimal mother wavelet for source localization eventually identified the sym20 mother wavelet as the best choice followed by bior6.8 and coif5.

Brain-Computer Interface (BCI) not only external permits controlling devices but also interacts using the environment by brain signals. EEG signals measurements over the motor cortex exhibit changes in power related to the movements or imaginations which are executed in motor tasks [

To accurately study and analyze the human brain, electroencephalography (EEG) [

The EEG signal main human brain frequencies.

EEG bands | Frequency (Hz) | Main description | |
---|---|---|---|

Delta | 0–4 | Deep state of sleep | |

Theta | 4–8 | Deep meditation and lucid dreaming | |

Alpha | 8–12 | Relaxation/creativity | |

Beta | 12–32 | Analytical thinking or stress/anxiety | |

Gamma | Lower | 32–64 | Wide brain activities or higher 64–128 brain disorder |

Higher | 64–128 |

The research community took an omnidirectional approach throughout the recent years to try to extract the human brain activities and access these five different frequency subbands. In this context, Murali et al. [

For their part, Tzimourta et al. [

The EEG signal is a nonstationary signal; the advantage of using the wavelet transform over the usual Fourier transform in EEG signals is their capability to analyze nonstationary signals [

Comparison between the partition of Fourier transform and wavelet transform in the time-frequency domain. (a) Fourier transform. (b) Wavelet transform.

In this context, this study aims at comparing 51 different mother wavelets using SWT to extract human brainwaves and localize their sources. In section

Influenced by the morphology and the structure of actual EEG signals, we created a sinusoidal signal with oscillations of 400 ms on 800 ms time windows used in the evaluation process.

A sampling rate of 1000 Hz and an oscillation frequency of 3, 6, 10, 20, and 45 Hz were recorded for the extraction of Delta, Theta, Alpha, Beta, and Gamma waves, respectively. The signal to the noise ratio (SNR) was also altered from −5 to 15 dB with −5 dB for noisy signal simulation, 10 dB for balanced signals, and 15 dB for acceptable quality signals. On the other hand, the amplitude of the signal depends on both the SNR value and the noise contaminating the signal, which is what is known as a pink noise; besides, it is a very common noise for biological systems.

The EEG signal dataset used in this study is a one-subject recording of a presurgical EEG signal from a pharmacoresistant subject with asymptomatic focal cortical dysplasia in the right occipital-temporal junction. The acquisition and preprocessing phases were applied as in our previous work [

Similar to the Fourier transform (FT), the wavelet transform (WT) is a function that grants the passage from the time to the frequency domain. However, the FT decomposes the signal into a series of sinus and cosines components as in the following equation:

The wavelet transform also decomposes the signal into a series of wavelet component as in the following equation:

Comparison between (a) FT decomposition component and different mother wavelets families decomposition components. (b) Symlets 4 (c) Coiflets 5. (d) Daubechies 11.

On the other hand, the wavelet transform used in this study is the stationary one (SWT) instead of the Continuous Wavelet Transform (CWT) or the Discrete Wavelet Transform (DWT). In fact, the SWT is more suitable for our case by avoiding the frequency band overlapping of CWT [

In order to decompose the EEG signal of our dataset that has 2500 Hz sampling rate to extract the five EEG frequency subbands, we had to reduce the signal to exactly 2048 Hz sampling rate; otherwise, these subbands would be extremely overlapping. In Figure

EEG signal SWT decomposition levels with cAi as the approximated coefficients and cDi as the detailed coefficients.

As the wavelet decomposition phase is completed, we evaluate the mother wavelets used in this process and move on to the source localization. Figure

The cycle of processing steps during this study.

The goodness of fit (GOF) is an evaluation method commonly used for physiological signals that adopt Pearson’s chi-squared statistical test [_{f}(

The Power Spectral Density is a display of the data energy distribution throughout the frequency spectrum. It is used as a visual evaluation process for its efficiency in presenting the data in the frequency domain rather than the time domain, which allows the identification of the extracted EEG frequency bands [

On the other hand, the scalp topographies are another visual evaluation process since it represents a mapping of the brain activities distributed on the surface of the scalp. An increasingly dipolar topography suggests that a cerebral measurement is an observation of a discharge operation involving a big number of neurons. Even in nonepileptic observations of brain activities, the dipolar scalp topographies are a great indicator of a valuable recording session since they reflect the domination of certain areas over others in the energetic exertion, which is the typical and more natural habit of cerebral behavior [

The source localization is an estimation of the brain activity generator locations [

In fact, the source localization process is sensitive to the quality of the extracted EEG frequency band and can also serve as an evaluation process that depends on the number of the located sources and the accuracy of their localization.

The goodness of fit (GOF) is the evaluation process that enabled us to minimize both our wavelet selection and processing criteria. Considering that the other evaluation methods and the source localization are a computationally heavy and costly process, the GOF is an excellent fast evaluation that relieved us from repeating the hull processing steps and source localization for the vast number of 51 mother wavelets. Figure

The GOF results in alpha and gamma waves with 51 mother wavelets using SNR values of −5, 10, and 15 dB.

On the other hand, the use of alpha and gamma wave extraction in GOF evaluation is justified by our earlier knowledge during our previous study [

The GOF results showed a similar pattern across the different frequency subbands and different SNR values with a distinct superiority to sym20, coif5, bior6.8, rbio6.8, and dmey wavelets.

In order to explore and investigate this superiority, we have extracted the best mother wavelets of every wavelet family and the wavelets that already showed some noteworthy results in other studies, such as sym4 in [

The results of the average GOF for every EEG frequency subband with the selected mother wavelets across the SNR values of −5, 10, and 15 dB.

Besides, after isolating the GOF results about the limited number of noteworthy wavelets, we notice that the performance of the wavelet extraction changes from one frequency subband to another with an obvious preeminence in gamma and alpha waves. We also observe that sym4 in [

Finally, to lock the GOF evaluation results, we calculated the noteworthy wavelet average across the five frequency subbands and ordered them from the lowest performance, on the left, to the best performance, on the right by their GOF score in Figure

The GOF average of the noteworthy wavelets across the EEG frequency subbands and SNR values ranked from left to right by order of best performance.

The Power Spectral Density (PSD) is also an important evaluation method that grants us a visual representation of the EEG signal extraction. The choice of frequency subband extraction visualization for this evaluation was limited to the alpha and gamma waves for the confirmed potential of SWT in their extraction. Moreover, due to the weak energy of the gamma wave and its proximity to the 50 Hz noise artifact of the original EEG signal dataset, we relied only on the alpha wave in the PSD visualization as it provides a clear display of the extraction effectiveness difference between the selected mother wavelets.

In Figure

PSD visualization of the different noteworthy mother wavelets in alpha wave extraction.

For the scalp topography visualization, almost all the noteworthy mother wavelets selected by the GOF had similar good results by producing depolarized scalp topographies isolated from the other frequencies, except for the Haar and sym4 wavelet extractions, which produced some interfering artifacts that could compromise the ability to review the scalp topographies by the medical experts and mislead them in diagnosing the cause of these parasites. Figure

A scalp topographies comparison between the original dataset, the noteworthy mother wavelets extractions, and the contaminated scalp topographies of Haar and sym4 wavelets for the five EEG frequencies subbands.

For the source localization, we performed the Independent Component Analysis (ICA) on the extracted signals by the noteworthy mother wavelets; then, we used the BEM for the forward problem and ECD for the inverse problem. As we have already mentioned, the ICA is a computationally costly process for feature extraction, especially with 62 EEG channels for the extraction of the same number of components before the source localization, so we reduced the process to include only the alpha and gamma frequency subbands. The alpha wave is the most important brainwave activity in the human brain and the gamma wave is perceived as an indicator of high active cognitive state and constantly used in brain malfunction and disease confirmation [

The ICA was performed using the runica algorithm from the EEGLAB toolbox [

Visualization of the alpha and gamma waves source localization using the noteworthy mother wavelets extractions.

Figure

The number of components localized by the noteworthy mother wavelets in alpha and gamma waves with RV under 15%.

An interpretation of the number of localized component results showed that the sym20 mother wavelets produced the best results followed by Haar and bior6.8, while coif5 had the lowest number of localized components.

In Figure

The number of times each mother wavelet scored the best accuracy for source localization in alpha and gamma waves.

The sym20 mother wavelet scored the best accuracy results followed by Haar and sym9, while rbio 6.8 did not have even once the best accuracy compared to the other wavelets for both frequency subbands. We also spot that the original EEG signal had an impressive accuracy in gamma wave, which indicates the interference of the other frequency subbands or the 50 Hz noise artifact and compromised the integrity of the located sources considering that the gamma wave had poor frequency energy that could not produce such result.

Table

The RV average of 5 first components for the noteworthy mother wavelets.

Wavelet | Alpha RV average of 5 first components | Gamma RV average of 5 first components | Combined RV average of best 5 first components |
---|---|---|---|

Original dataset | 10.8 | ||

Sym4 | 8.9 | 9.5 | 8.6 |

Sym6 | 7.8 | 9.6 | 7.7 |

Sym9 | 6.8 | 10.2 | 6.8 |

Sym20 | 9.4 | 9.6 | 6.2 |

Haar | 10.9 | 8.3 | 6.7 |

Db5 | 7.8 | 9.7 | 7.8 |

Coif5 | 8.8 | 10.2 | 6.2 |

Bior6.8 | 6.7 | 9.6 | 6.6 |

Rbio6.8 | 9.3 | 10.4 | 9.3 |

demy | 9.4 | 9.6 | 6.8 |

Actually, the best result for the alpha wave was achieved by bior6.8 while the worst was recorded by the Haar mother wavelet. For the gamma wave, the Haar mother wavelet produced the best result, while rbio6.8 extractions were last compared to the other wavelet extractions. Then, regarding the combined best-localized components of alpha and gamma, the sym20 and coif5 shared the first place in extracting the most accurate first five components, with the rbio6.8 mother wavelet in the last place.

As an overall perception of the source localization results in evaluating our mother wavelets, we can classify the sym20 mother wavelet as the best mother wavelet extraction overall, while the Haar occupies the second place with questionable results due to our previous readings of the GOF, PSD, and scalp topographies that proved the interference of frequency overlapping and noise artifacts in the sincerity of the localized components. If we eliminate the Haar mother wavelet, we must crown the bior6.8 mother wavelet the second place considering the number of localized components and the best results achieved in the accuracy average of the first components in the alpha wave followed by the coif5 and sym9 mother wavelets. While On the other hand, the dmey produced a somehow moderate result in light of the promising potential in the earlier evaluations of GOF, PSD, and scalp topographies. The least favorite mother wavelet in source localization was the rbio6.8 with the worst accuracy results recorded by all the noteworthy mother wavelets.

In this paper, we have compared 51 different mother wavelets taken from 7 different families including Haar, Symlets, Daubechies, Coiflets, Discrete Meyer, Biorthogonal, and reverse Biorthogonal, which are applied to source localization and extraction of EEG signal. For the source localization performance comparison, the 10 mother wavelets selected from the 51 mother wavelets produced an adequate result. However, the sym20 outshined all the other wavelets and took the lead almost in every evaluation followed by a notable performance from bior6.8, coif5, and sym9, respectively. Then, the least results were produced by the Haar and rbio6.8 mother wavelets. As a conclusion, the Symlet family generates the top results for EEG signal, as demonstrated by our study. Then, bior6.8 and coif5 are the second important mother wavelets for source localization.

Regarding the evaluation methods, we used the goodness of fit (GOF), the Power Spectral Density, and scalp topographies in the extraction of EEG frequency subbands applied to benchmarks containing source localization with the number of located sources and accuracy of localization. The source localization is produced via Stationary Wavelet Transform (SWT) and an Independent Component Analysis (ICA) feature extraction followed by Boundary Element Model (BEM) and Equivalent Current Dipole (ECD) solutions for the forward and inverse problem. Future studies and advancements could explore the improvement of the source localization feature extraction or forward and inverse problem solutions. The use of artificial intelligence techniques based on the deep neural network could help to facilitate the simulation and give better results.

The medical used data are available from the corresponding author upon request.

The authors declare no conflicts of interest.

Dr. Omar Cheikhrouhou thanks Taif University for its support under the project Taif University Researchers Supporting Project no. TURSP-2020/55, Taif University, Taif, Saudi Arabia.