# Enhanced Automatic Wavelet Independent Component Analysis for Electroencephalographic Artifact Removal

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## Abstract

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## 1. Introduction

## 2. Methodology: Enhanced Automatic Wavelet-ICA

#### 2.1. EAWICA Description:

#### 2.1.1. EEG Rhythm (Wavelet Components) Extraction Through DWT

#### 2.1.2. Automatic Artifactual WCs Selection

_{n}is the n-order central moment of the variable and m

_{1}is the mean. Kurtosis is positive for “peaked” distributions (eye blink, cardiac artifacts, etc.), whereas it is negative for “flat” activity distributions (noise [28]).

_{1},…,X

_{n}}. In case of a very random signal (i.e., the component accounting for noisy background activity), the probabilities will be uniformly distributed and the entropy will be low (because the argument of the logarithm tends to n/2 ≥ 1). In case of no random signal (signal accounting for a transient event), most of the values will have high probability and some values (those which occurred during the transient event) will have low probability; the overall contribution to entropy will be high (the argument of the logarithm tends to zero). Here, the random variables whose entropy will be estimated are the WCs (Step 2 in Figure 1) and the WICs (Step 3 in Figure 1). For a random variable x, with N given samples, Renyi’s entropy is defined as:

_{σ}is the kernel function and indexes i and j range from 1 to N, the number of samples in the Parzen window [29]. This is the formula that was used, together with kurtosis, in Steps 2 and 4 of Figure 1.

#### 2.1.3. Wavelet Independent Components Extraction

**x**,

**x**is passed through ICA in order to extract the set

**u**of wavelet independent components (WICs). The INFOMAX algorithm, particularly suitable for EEG processing [30,31], was selected to perform ICA. In order to properly take into account either sub-Gaussian and super-Gaussian signals, the extended-INFOMAX version was used [32].

#### 2.1.4. Automatic Artifactual WICs Selection

**u**) need to undergo a process of estimation of their degree of “artifactuality”. In order to classify a WIC (row of matrix

**u**) as artifactual or not, every WIC was divided into 1-s non-overlapping segments (named “epochs”), and two markers (kurtosis and entropy) were estimated for each epoch and for each WIC. Once each marker has been estimated and arranged as a n × m matrix, where n is the number of WICs and m is the number of epochs, the columns were normalized to zero-mean and unitary standard deviation, so that, within each epoch, the marker value of a WIC is compared to the same marker values of every other WIC. The WICs whose kurtosis or entropy exceeded a fixed threshold (Th2) in more than 20% of the epochs are selected, but not rejected. The threshold 20% is chosen according to [33].

#### 2.1.5. Artifactual Epochs Rejection

#### 2.1.6. Reconstruction

_{af}) and inverse DWT to reconstruct the artifact-free WCs. Finally, the overall artifact-free EEG dataset is reconstructed. Inverse ICA can be performed multiplying u

_{af}by the inverse of the estimated unmixing matrix W, so that the dataset of WCs is reconstructed, discarding artifactual epochs. (x

_{rec}).

_{rec}are restored in the original WCs dataset. Then, the inverse DWT is performed in order to reconstruct the “clean” EEG recording.

#### 2.2. EEG Data Description:

#### 2.2.1. Semi-Simulated EEG

#### 2.2.2. Real EEG

## 3. Method Optimization

## 4. Results

#### 4.1. AWICA and EAWICA Optimization

#### 4.2. Test on Semi-Simulated EEG

#### 4.3. Test on Real EEG

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Description of the block diagram of the enhanced-wavelet-ICA (EAWICA) processing system for EEG artifact rejection. The EEG recording is first partitioned into the four major EEG brain waves, and the wavelet components (WCs) are extracted. The subset of artifactual WCs is then selected, passed through ICA, and the independent components (WICs) are extracted. The WICs affected by artifacts are detected by entropy and kurtosis and then passed through a further step: the automatic rejection of the artifactual epochs. Inverse ICA and wavelet reconstruction are then performed in order to recover an artifact-free EEG dataset. The blocks are numerically labeled according to the corresponding subsections of Section 2.

**Figure 2.**The independent components wavelet independent components (WICs) extracted during the processing of the dataset affected by eye blink artifacts.

**Figure 3.**The WICs shown in Figure 2 after they have been processed and cleaned by AWICA.

**Figure 4.**The WICs shown in Figure 2 after they have been processed and cleaned by EAWICA.

**Figure 5.**Wavelet decomposition tree used for the simulated artifactual EEG dataset. The legend illustrates which details are used to reconstruct the brain waves. Since the frequency band was 0–50 Hz, a small approximation was used to reconstruct delta, theta and alpha bands.

**Figure 6.**Wavelet decomposition tree used for the real EEG dataset. The legend illustrates which details are used to reconstruct the brain waves.

**Figure 7.**AWICA vs. EAWICA performance comparison for different Th1-Th2-α settings and different kinds of artifacts: eye blink (

**top-left**); muscular activity (subplot top-right); electrical shift (

**bottom-left**); linear trend (

**bottom-right**). The original artifact-free EEG and the final reconstructed EEG are compared. The parameters used to compare the two signals are the peak-SNR and the RMSE (the settings corresponding to the largest PSNR and the smallest RMSE ensures the best performance and is defined as optimal). The x-axis accounts for percentual RMSE (referring to the overall largest RMSE, when the results of either AWICA and EAWICA are considered), and the y-axis accounts for percentual PSNR (referring to the overall largest PSNR, when the results of either AWICA and EAWICA are considered). The results yielded by AWICA are represented by a red (o), whereas the results yielded by EAWICA are represented by a blue (+).

**Figure 8.**Visual comparison between the performance of AWICA and EAWICA in the artifact rejection. Once the optimal Th1-Th2-α configuration was selected for either AWICA and EAWICA, the two techniques were tested against each other over the four semi-simulated artifactual EEG dataset (EEG with eye blink, muscle activity, electrical shift and linear trend). Each subplot shows the original artifact-free EEG, the EEG with the simulated artifact and the EEG reconstructed after artifact rejection. For eye blink removal, the channels involved are: Fp1 (Ch1) and Fp2 (Ch2). For the other artifacts, the channels involved are C3 (Ch1) and C4 (Ch2). The left column shows the results of AWICA artifact removal, whereas the right column shows the results of EAWICA artifact removal. EAWICA removed eye blink artifact and muscular activity better than AWICA; furthermore, it removed electrical shift and linear trend artifacts with a lesser distortion and attenuation of the EEG, especially in the artifact-free segments.

**Figure 9.**Comparison among the power spectral density (PSD) of the artifact-free EEG and the PSD of the corresponding EEG reconstructed by AWICA and by EAWICA. The two techniques were tested against each other over the four semi-simulated artifactual EEG dataset (EEG with eye blink, muscle activity, electrical shift and linear trend). Each subplot corresponds to a different artifact removal and shows the three PSDs (original artifact-free EEG, EEG reconstructed by AWICA and EEG reconstructed by EAWICA).

**Figure 10.**EAWICA performance on artifact removal from real EEG. EAWICA was applied with the Th1-Th2-α overall optimal configuration that provided relatively high PSNR in the removal of each artifact (see Section 4.3). Each subplot in the left column shows an example of the artifact that occurred in the real EEG, and the corresponding subplot on the right column shows the EEG cleaned by EAWICA.

**Figure 11.**EAWICA performance on artifact removal from real EEG. EAWICA was applied with the Th1-Th2-α overall optimal configuration that provided relatively high PSNR in the removal of each artifact (see Section 4.3). Each subplot in the left column shows an example of the artifact that occurred in the real EEG, and the corresponding subplot on the right column shows the EEG cleaned by EAWICA.

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Mammone, N.; Morabito, F.C. Enhanced Automatic Wavelet Independent Component Analysis for Electroencephalographic Artifact Removal. *Entropy* **2014**, *16*, 6553-6572.
https://doi.org/10.3390/e16126553

**AMA Style**

Mammone N, Morabito FC. Enhanced Automatic Wavelet Independent Component Analysis for Electroencephalographic Artifact Removal. *Entropy*. 2014; 16(12):6553-6572.
https://doi.org/10.3390/e16126553

**Chicago/Turabian Style**

Mammone, Nadia, and Francesco C. Morabito. 2014. "Enhanced Automatic Wavelet Independent Component Analysis for Electroencephalographic Artifact Removal" *Entropy* 16, no. 12: 6553-6572.
https://doi.org/10.3390/e16126553