Sensor-space EEG analyses typically rely on electrode layouts or data-driven components and rarely encode cortical geometry, making scalp patterns difficult to link to anatomy and to compare across participants. We introduce a sensor-space basis dictionary that explicitly integrates cortical geometry. Laplace-Beltrami (LB) eigenmodes are computed on a standard cortical template (fsaverage) and mapped by the lead-field matrix of a three-layer boundary-element (BEM) head model to yield cortex-anchored sensor-space harmonics. The leadfield-mapped LB dictionary spans scalp topographies, while preserving a meaningful spatial-frequency ordering inherited from the cortical manifold. We assess representational efficiency using ordinary least squares (OLS) projections of resting EEG (eyes-closed/open) across 59-, 32-, and 19-channel montages, and compare against spherical harmonics (SPH), principal components (PCA), and independent components (ICA). Efficiency is quantified by the variance explained of spatial configuration <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R^2(K)\)</EquationSource> </InlineEquation> (by leading K modes) and the efficiency indices <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(K_{70}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(K_{90}\)</EquationSource> </InlineEquation> (fewest modes reaching <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(R^2\!\ge \!0.70\)</EquationSource> </InlineEquation> and 0.90) and between-condition consistency by ICC(3,1) of eyes-open/closed coefficients. The cortex-anchored basis shows higher early-K <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation> than SPH and PCA (e.g., 59-channel eyes-closed at <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(K{=}4\)</EquationSource> </InlineEquation>: LB <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(R^2\!\approx \!0.56\)</EquationSource> </InlineEquation> [95% CI: 0.54, 0.59] vs. SPH <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\approx \!0.44\)</EquationSource> </InlineEquation> [0.42, 0.46], PCA <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\approx \!0.08\)</EquationSource> </InlineEquation> [0.07, 0.09]) and reaches 70% and 90% variance with fewer modes (LB <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(K_{70}\!\approx \!8.6\)</EquationSource> </InlineEquation>; SPH <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\approx \!12.3\)</EquationSource> </InlineEquation>; PCA <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(\approx \!19.3\)</EquationSource> </InlineEquation>; ICA <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(\approx \!22.8\)</EquationSource> </InlineEquation>; LB <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(K_{90}\!\approx \!22.6\)</EquationSource> </InlineEquation>; SPH <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(\approx \!25.3\)</EquationSource> </InlineEquation>; PCA <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(\approx \!23.2\)</EquationSource> </InlineEquation>; ICA <InlineEquation ID="IEq17"> <EquationSource Format="TEX">\(\approx \!30.2\)</EquationSource> </InlineEquation>). Mode-wise coefficient consistency (eyes-open vs. eyes-closed) is comparable between LB and SPH. By combining cortical eigenmodes with a forward head model, this approach yields a geometry-aligned, interpretable representation of sensor-space EEG that offers superior fidelity-complexity trade-offs at small K and a principled scaffold for low-dimensional EEG sensor space analysis.

Forward-Projected Cortical Eigenmodes Provide an Efficient Sensor-Space Representation of Resting-State EEG

期刊论文
发表日期：

2026年3月24日

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Hyung G. Park

摘要

Sensor-space EEG analyses typically rely on electrode layouts or data-driven components and rarely encode cortical geometry, making scalp patterns difficult to link to anatomy and to compare across participants. We introduce a sensor-space basis dictionary that explicitly integrates cortical geometry. Laplace-Beltrami (LB) eigenmodes are computed on a standard cortical template (fsaverage) and mapped by the lead-field matrix of a three-layer boundary-element (BEM) head model to yield cortex-anchored sensor-space harmonics. The leadfield-mapped LB dictionary spans scalp topographies, while preserving a meaningful spatial-frequency ordering inherited from the cortical manifold. We assess representational efficiency using ordinary least squares (OLS) projections of resting EEG (eyes-closed/open) across 59-, 32-, and 19-channel montages, and compare against spherical harmonics (SPH), principal components (PCA), and independent components (ICA). Efficiency is quantified by the variance explained of spatial configuration \(R^2(K)\) (by leading K modes) and the efficiency indices \(K_{70}\) and \(K_{90}\) (fewest modes reaching \(R^2\!\ge \!0.70\) and 0.90) and between-condition consistency by ICC(3,1) of eyes-open/closed coefficients. The cortex-anchored basis shows higher early-K \(R^2\) than SPH and PCA (e.g., 59-channel eyes-closed at \(K{=}4\) : LB \(R^2\!\approx \!0.56\) [95% CI: 0.54, 0.59] vs. SPH \(\approx \!0.44\) [0.42, 0.46], PCA \(\approx \!0.08\) [0.07, 0.09]) and reaches 70% and 90% variance with fewer modes (LB \(K_{70}\!\approx \!8.6\) ; SPH \(\approx \!12.3\) ; PCA \(\approx \!19.3\) ; ICA \(\approx \!22.8\) ; LB \(K_{90}\!\approx \!22.6\) ; SPH \(\approx \!25.3\) ; PCA \(\approx \!23.2\) ; ICA \(\approx \!30.2\) ). Mode-wise coefficient consistency (eyes-open vs. eyes-closed) is comparable between LB and SPH. By combining cortical eigenmodes with a forward head model, this approach yields a geometry-aligned, interpretable representation of sensor-space EEG that offers superior fidelity-complexity trade-offs at small K and a principled scaffold for low-dimensional EEG sensor space analysis.