29.04.2019 | Review | Ausgabe 4/2019 Open Access

# Which Reference Should We Use for EEG and ERP practice?

- Zeitschrift:
- Brain Topography > Ausgabe 4/2019

## Publisher's Note

## Background

## The EEG/ERP Reference Problem

### No Constant Point on the Scalp Surface

_{∞}known as the lead field matrix, expresses the forward model theoretically computed with the infinity reference.

### General Form of the Reference Problem

_{r}is a non-stochastic matrix of observations, φ are potentials with the infinity reference, supposed to be a deterministic, fixed but unknown vector, ε are non-observable random sensor noise disturbances (Hu et al. 2019). The EEG reference problem in (3) is apparently an underdetermined linear regression problem.

_{r}and ε are considered to have the multivariate normal distribution. If the sensor noise has an independent identical distribution (IID) across channels, the covariance of the sensor noise in the referenced data will be \(\varSigma_{{{\varvec{\upvarepsilon}}_{r} {\varvec{\upvarepsilon}}_{r} }} = \sigma^{2} {\mathbf{T}}_{r} {\mathbf{T}}_{r}^{{\mathbf{T}}}\), because referencing effect is taken on the noise as well during recording (Pascual-Marqui et al. 1994; Hu et al. 2018c).

_{r}of unipolar references is the overwhelming body of the EEG reference issue, as its goal is to approach the ideal potential with infinity reference. Besides, T

_{r}can also be the 1st derivative in the bipolar recordings, which is proportional to the local current density between two adjacent electrodes and the 2nd differential operator in the scalp Laplacian, a possible approximation to the current source density. The latter two are different physical quantifications from EEG potentials.

### Indeterminacy Principle of Scalp EEG

## Theory of Unipolar References

_{r}are all full rank deficent by 1 for all the unipolar references, and ‘orthogonal projector centering’.

### Recording Reference (RR)

### Linked Mastoids (LM)

### Average Reference (AR)

_{r}is always singular (Hu et al. 2019). The estimation of φ in (3) is thus a generalized linear inverse problem. The minimum Euclidean norm solution is the special case of (4) with the prior \({\varvec{\Sigma}}_{{{\mathbf{\varphi \varphi }}}} = \alpha^{2} {\mathbf{I}}_{{N_{c} }}\) and the assumption σ

^{2}tends to zero (Hu et al. 2018c). Thus, the solution finally simplifies to

_{r}is same as applying the AR to the potentials with infinity reference. It also confirms that AR can only be applied to the recorded data that was already transformed by the other unipolar references (Hu et al. 2018a).

### Reference Electrode Standardization Technique (REST)

^{2}tends to 0, say, the case of noise free data, it turns as the REST transforming

_{r}and the equivalent source is approximately estimated as \({\hat{\mathbf{s}}} = {\mathbf{G}}_{r}^{ + } {\mathbf{v}}_{r}\) (Yao 2001).

Unipolar Reference | Electrode density | Electrode coverage | Head model (shape, inner conductivity) | |
---|---|---|---|---|

Online | Cz, Pz, etc. | |||

Offline | LM | |||

REST | √ | √ | √ | |

AR | √ | √ | √ |

_{r}and the sources positions. The goal of REST is not to find the actual sources which one does not need to disentangle. One may take a closed distributed dipole layer with all actual sources inside as the equivalent sources (Yao 2000b; Yao and He 2003). Then (10) is a linear equation from the scalp data \({\mathbf{v}}_{r}\) to the strengths of the equivalent sources with fixed positions. Since the number of sources is usually much larger than the decayed rank in \({\mathbf{G}}_{r}\), (10) is an undetermined system. Thus, the pseudoinverse of \({\mathbf{G}}_{r}\) can be adopted to get the minimum norm solution to \({\mathbf{s}}\). Equation (10) also shows us that the sources \({\mathbf{s}}\) just play a role of bridge from \({\mathbf{v}}_{r}\) to φ. However, this bridge does lend the chance for REST from any unipolar reference recordings to φ at infinity (Yao 2001).

## Comparison of Unipolar References by Simulations

### Reconstruction of the Reference Signal

### Sensitivity to Errors in the Head Model

### Sensitivity to Neural Source Position

### Sensitivity to the SNR and Head Model

## Impact of the Unipolar Reference on Real Data Analysis

### Evaluation of the References by Statistical Information Criteria

### On the Power Spectra of EEG

### On the Amplitude of the ERP

### On the Latency of ERP

## Non-unipolar References

### Bipolar Recordings

^{st}order derivative of the potential. According to theory of electric field, it is a metric related to tangential current density over the scalp surface, not a potential at all, as illustrated by (16). Obviously, it depends on the montage. It is more sensitive to noise than to EEG signal, and less sensitive to signal from deep neural source because the derivative-like operation acts as a high pass filter. Bipolar recordings are mainly used in clinic to “enhance” focal activity (Niedermeyer and Da Silva 2005).