Cortex-anchored sensor-space harmonics for event-related EEG

Objective.Scalp event-related potentials (ERPs) measured with electroencephalography (EEG) are temporally precise but spatially bandwidth-limited: skull and scalp blur cortical activity, and event-related EEG is usually represented in electrode coordinates or dataset-specific data-driven components rather than in a sensor-space coordinate system linked to cortical anatomy. We aimed to develop and evaluate a cortex-anchored sensor-space basis for event-related EEG.Approach.We constructed a multiscale sensor-space dictionary by forward-projecting cortical Laplace-Beltrami (LB) eigenmodes through a realistic EEG head model, yielding basis functions ordered by increasing cortical spatial frequency. Using ERP-CORE (7 paradigms, 39 participants), we benchmarked the forward-projected LB basis against (i) spherical harmonics (SPH) defined on the same montage and (ii) group principal component analysis/independent component analysis bases learned from trial-averaged time-frequency (TF) maps. Across canonical components (N170, N2pc, N400, P3b, lateralized readiness potential (LRP), error-related negativity (ERN)), we quantified reconstruction efficiency (R2as a function of the number of modes), concentration of evoked TF energy across modes, split-half reliability of mode scores (ICC), and low-dimensional reconstruction of group-level ERP contrast topographies.Main results.LB closely matched SPH in reconstruction efficiency, but concentrated evoked TF energy more strongly in low-order modes. For N170, N400, P3b, and ERN, the first 10 LB modes captured about 70% of normalized TF energy, whereas SPH typically required 15-18 modes. Low-to-mid LB mode scores showed moderate-to-excellent reliability, often comparable to or slightly exceeding SPH. In addition, 10-15 LB modes reconstructed canonical ERP contrast maps with high correlations while preserving the expected sensor-space organization, including posterior N170, centro-parietal N400/P3, and fronto-central ERN patterns.Significance.Forward-mapped LB eigenmodes provide a compact, anatomy-linked sensor representation for event-related EEG that complements spherical and data-adaptive bases. The proposed sensor-space basis offers a reusable, geometry-informed coordinate system that captures whole-scalp ERP structure compactly while remaining linked to cortical spatial organization.