Removal of ocular artifacts from the EEG: a comparison between time-domain regression method and adaptive filtering method using simulated data

Abstract

We recently proposed an adaptive filtering (AF) method for removing ocular artifacts from EEG recordings. The method employs two parameters: the forgetting factor λ and the filter length M. In this paper, we first show that when λ = M = 1, the adaptive filtering method becomes equivalent to the widely used time-domain regression method. The role of λ (when less than one) is to deal with the possible non-stationary relationship between the reference EOG and the EOG component in the EEG. To demonstrate the role of M, a simulation study is carried out that quantitatively evaluates the accuracy of the adaptive filtering method under different conditions and comparing with the accuracy of the regression method. The results show that when there is a shape difference or a misalignment between the reference EOG and the EOG artifact in the EEG, the adaptive filtering method can be more accurate in recovering the true EEG by using an M larger than one (e.g. M = 2 or 3).

Appendix: The case of M = λ = 1 in adaptive filtering

Let us consider a simplest case of the adaptive filtering method where M = λ = 1. In this case, Eq. (3) becomes:

$$ \varepsilon (n) = {\sum\limits_{i = 1}^n {e^{2} (i)} } = {\sum\limits_{i = 1}^n {{\left[ {y(i) - h_{{\text{v}}} r_{{\text{v}}} (i) - h_{{\text{h}}} r_{{\text{h}}} (i)} \right]}} }^{2} $$

(8)

The two filter coefficients, h _v and h _h , that minimize ε(n) can be obtained by solving the following two equations:

$$ {\sum\limits_{i = 1}^n {y(i)r_{{\text{v}}} (i) = h_{{\text{v}}} {\sum\limits_{i = 1}^n {r_{{\text{v}}} ^{2} (i) + \,} }} }h_{{\text{h}}} {\sum\limits_{i = 1}^n {r_{{\text{v}}} (i)\,r_{{\text{h}}} (i)} } $$

(9)

$$ {\sum\limits_{i = 1}^n {y(i)r_{{\text{h}}} (i) = h_{{\text{h}}} {\sum\limits_{i = 1}^n {r_{{\text{h}}} ^{2} (i) + \,} }} }h_{{\text{v}}} {\sum\limits_{i = 1}^n {r_{{\text{v}}} (i)\,r_{{\text{h}}} (i)} } $$

(10)

Equations (9) and (10) are identical to the two equations used by Quilter et al. [11] for removing EOG artifacts based on the least squares principal, albeit the variable notations were different. As a result, for the same set of the EEG and reference EOG data, the adaptive filtering method and the time-domain regression method produce exactly the same transmission coefficients. In this case, the only difference between the two methods is in implementation: while the TR method is applied once to the entire set of the collected data (the entire epoch), the AF method is implemented for sample-by-sample updating filter coefficients and removal of the EOG artifacts, starting from the beginning of data collection.