Removal of Muscle Artifacts from EEG Recordings of Spoken Language Production

Abstract

Research on the neural basis of language processing has often avoided investigating spoken language production by fear of the electromyographic (EMG) artifacts that articulation induces on the electro-encephalogram (EEG) signal. Indeed, such articulation artifacts are typically much larger than the brain signal of interest. Recently, a Blind Source Separation technique based on Canonical Correlation Analysis was proposed to separate tonic muscle artifacts from continuous EEG recordings in epilepsy. In this paper, we show how the same algorithm can be adapted to remove the short EMG bursts due to articulation on every trial. Several analyses indicate that this method accurately attenuates the muscle contamination on the EEG recordings, providing to the neurolinguistic community a powerful tool to investigate the brain processes at play during overt language production.

Appendix: CCA

Ordinary correlation analysis quantifies the relation between (realizations of) two variables a(t) and b(t) by means of a correlation coefficient ρ:

$$ \rho=\frac{Cov[{\bf a},{\bf b}]}{\sqrt{V[{\bf a}]V[{\bf b}]}} \label{eq:correlatie} $$

(6)

in which Cov and V indicate respectively the co—and variance. CCA is a multivariate extension of ordinary correlation analysis.

Consider 2 multivariate zero-mean vectors $\textbf{A}$ and $\textbf{B}$, and two new scalar variables, $\tilde{\bf a}$ and $\tilde{\bf b}$, generated as linear combinations of the components in $\textbf{A}$ and $\textbf{B}$:

$$ \begin{array}{lll} \textbf{A}&=&[{\bf a}_1(t), \ldots , {\bf a}_m(t)]^T\\ \textbf{B}&=&[{\bf b}_1(t), \ldots , {\bf b}_n(t)]^T, t=1, .., N\\ \tilde{\bf a} &=& w_{{\bf a}_{1}}{\bf a}_1 + \ldots + w_{{\bf a}_{m}}{\bf a}_m = \textbf{w}_{\bf a}^T \textbf{A} \\ \label{eq:y}\tilde{\bf b} &=& w_{{\bf b}_{1}} {\bf b}_1 + \ldots + w_{{\bf b}_{m}} {\bf b}_m = \textbf{w}_{\bf b}^T\textbf{B} \end{array} $$

(7)

CCA computes the coefficients $\textbf{w}_{\bf a}$ and $\textbf{w}_{\bf b}$ that maximize the correlation between $\tilde{\bf a}$ and $\tilde{\bf b}$. These coefficients are the regression weights and $\tilde{\bf a}$ and $\tilde{\bf b}$ are denoted as canonical variates. The resulting correlation coefficient is the canonical correlation coefficient.

It can be shown that finding these regression weights correspond to solving an eigen value problem.

By inserting Eq. 7 into the definition of the correlation coefficient (6), and assuming the means of $\textbf{A}$ and $\textbf{B}$ zero, we obtain:

$$ \rho = \frac{\textbf{w}_{\bf a}^T \textbf{C}_{{\bf a}{\bf b}} \textbf{w}_{\bf b}}{\sqrt{( \textbf{w}_{\bf a}^T \textbf{C}_{{\bf a}{\bf a}} \textbf{w}_{\bf a} ) (\textbf{w}_{\bf b}^T \textbf{C}_{{\bf b}{\bf b}} \textbf{w}_{\bf b}) }} $$

(8)

with $\textbf{C}_{{\bf a}{\bf a}}$ and $\textbf{C}_{{\bf b}{\bf b}}$ the variance matrices from respectively $\textbf{A}$ and $\textbf{B}$ and $\textbf{C}_{{\bf a}{\bf b}}$ the covariance matrix from $\textbf{A}$ and $\textbf{B}$. ρ is a function of $\textbf{w}_{\bf a}$ and $\textbf{w}_{\bf b}$. In order to maximise the correlation coefficients , we impose the partial derivatives with respect to $\textbf{w}_{\bf a}$ and $\textbf{w}_{\bf b}$ to be zero. This results in following system:

$$ \begin{array}{lll} \label{ccaoplossing} \textbf{C}_{{\bf a}{\bf a}}^{-1} \textbf{C}_{{\bf a}{\bf b}} \textbf{C}_{{\bf b}{\bf b}}^{-1} \textbf{C}_{{\bf b}{\bf a}} \textbf{w}_{{\bf a}_i}= \rho ^2 \textbf{w}_{{\bf a}_i} \\ \textbf{C}_{{\bf b}{\bf b}}^{-1} \textbf{C}_{{\bf b}{\bf a}} \textbf{C}_{{\bf a}{\bf a}}^{-1} \textbf{C}_{{\bf a}{\bf b}} \textbf{w}_{{\bf b}_i}= \rho ^2 \textbf{w}_{b_i} \end{array} $$

(9)

This system is an eigenvalue decomposition. The matrices $\textbf{C}_{{\bf a}{\bf a}}^{-1} \textbf{C}_{{\bf a}{\bf b}} \textbf{C}_{{\bf b}{\bf b}}^{-1} \textbf{C}_{{\bf b}{\bf a}}$ and $\textbf{C}_{{\bf b}{\bf b}}^{-1} \textbf{C}_{{\bf b}{\bf a}} \textbf{C}_{{\bf a}{\bf a}}^{-1} \textbf{C}_{{\bf a}{\bf b}}$ have the same eigenvalues. The vectors $\textbf{w}_{\bf a}$ and $\textbf{w}_{\bf b}$ we are looking for, are the eigenvectors corresponding to the highest eigenvalue. This eigenvalue is the square of the maximal correlation between the canonical variates.