regression-eog

name	regression_eog
description	Regression-based EOG removal — fast online ocular artifact suppression
layer	L3
group	adaptive_cleaning
metadata	{"tags":["operator","adaptive_cleaning","regression","eog","gratton","fast","online"],"modalities":["eeg","meg"],"step_string":"regression_eog","analysis_goal_allowed":["classification","source_localization","feature_extraction","clinical_screening","exploratory","generic","connectivity","online_inference"],"analysis_goal_forbidden":[]}

Regression-Based EOG Removal

Function

Linear regression of EOG channels out of EEG/MEG channels. Faster than ICA / SSP, no labelled events needed — the de-facto online BCI choice when an EOG channel is present. Originally Gratton et al. 1983.

Input / Output: (n_channels, n_times) → (n_channels, n_times) with EOG-related variance removed.

Algorithm & Math

β_c = argmin || data[c] − β · eog ||²
out[c] = data[c] − β_c · eog

Optionally per-band (Croft & Barry 2000): bandpass first, then regress per band.

Parameter Format & Defaults

regression_eog:{eog_ch}

Parameter	Type	Default	Description
eog_ch	str	"EOG"	EOG channel substring.
band (kw)	tuple	None	Optional per-band regression.

Modality-Specific Considerations

EEG: standard. MEG: viable (cardiac too via separate channel). sEEG / ECoG / fNIRS / spike: forbidden (no EOG analog).

When to Use / NOT to Use

Use when: online BCI; latency-critical; EOG channel present.

Don't use when: no EOG; PAC / connectivity require very precise preservation (use SSP or ICA).

Constraints & Ordering

• Apply after bandpass / drop_bads.
• Apply before epoching / decoder.
• EOG channel kept or dropped after (configurable).

Failure Modes & Detection

Failure	Symptom	Detection
EOG missing	KeyError.	Pre-check; raise recoverable.
Cross-talk overcorrection	Frontal EEG flattened.	If frontal alpha drop > 30% warn.

Common Issues

• "Frontal EEG looks flat." EOG-EEG correlation high; the regression removed real frontal signal. Use SSP / ICA for higher-quality removal.

Reference Implementation

Standalone

from __future__ import annotations
import numpy as np


def regression_eog(
    data: np.ndarray, eog_idx: int,
) -> np.ndarray:
    """Linear regression of EOG out of EEG."""
    eog = data[eog_idx]
    out = data.copy()
    eog_var = float(np.var(eog)) + 1e-30
    for c in range(data.shape[0]):
        if c == eog_idx: continue
        beta = float(np.dot(data[c], eog)) / (eog_var * data.shape[1])
        out[c] = data[c] - beta * eog
    return out.astype(data.dtype, copy=False)

EasyBCI-Adapted

from typing import Any, Dict
import time
import numpy as np
from easybci_lib.tools.neural_processing.operator_errors import EasyBCIOperatorError
from easybci_lib.tools.neural_processing.preprocess.step_cache import record_step_elapsed


def operator_regression_eog(
    data_dict: Dict[str, Any], *, eog_ch: str = "EOG",
) -> Dict[str, Any]:
    """Regression-based EOG removal.

    Parameters
    ----------
    data_dict : dict
    eog_ch : str

    Returns
    -------
    dict — cleaned data.

    Raises
    ------
    EasyBCIOperatorError
        recoverable=True if EOG channel absent.

    Modality coverage
    -----------------
    EEG / MEG: yes. Others: forbidden.

    References
    ----------
    Gratton et al. 1983; Croft & Barry 2000.
    """
    channels = data_dict.get("channels", [])
    eog_idx = next((i for i, c in enumerate(channels) if eog_ch.lower() in c.lower()), None)
    if eog_idx is None:
        raise EasyBCIOperatorError(
            operator="regression_eog", reason=f"no channel matching {eog_ch!r}",
            recoverable=True, fallback_step="ica",
        )

    t0 = time.monotonic()
    data = data_dict["data"]
    eog = data[eog_idx]
    eog_var = float(np.var(eog)) + 1e-30
    new_data = data.copy()
    for c in range(data.shape[0]):
        if c == eog_idx: continue
        beta = float(np.dot(data[c], eog)) / (eog_var * data.shape[1])
        new_data[c] = data[c] - beta * eog
    new_data = new_data.astype(data.dtype, copy=False)
    elapsed = time.monotonic() - t0

    out = dict(data_dict)
    out["data"] = new_data
    out["elapsed_s"] = elapsed
    out["meta"] = {**out.get("meta", {}), "regression_eog": {"eog_ch": eog_ch}}
    record_step_elapsed("regression_eog", elapsed, (data_dict.get("meta") or {}).get("step_cache_key"))
    return out

References

1. Gratton, G. et al. (1983). A new method for off-line removal of ocular artifact. EEG Clin. Neurophysiol. 55(4): 468–484. doi:10.1016/0013-4694(83)90135-9.
2. Croft, R. J., & Barry, R. J. (2000). Removal of ocular artifact from the EEG: a review. Neurophysiologie Clinique 30(1): 5–19. doi:10.1016/S0987-7053(00)00055-1.