Geometry-aware
A lead-field matrix derived from each subject's T1-weighted MRI constrains the source estimate.
Under review
CANDLE
Cortical-geometry Aware Null-space Decomposition for Localized ESI
Learning subject-specific cortical source activity from EEG by placing a data-driven prior only on what the measurements cannot observe.
Abstract
Electrophysiological source imaging estimates cortical activity from noninvasive EEG, but the problem is fundamentally ill-posed: source activity is much higher-dimensional than sensor observations.
We introduce CANDLE, a learning-based ESI model that preserves subject-specific geometric constraints while learning a prior over the unobservable null space. Trained exclusively on a new whole-brain simulator, CANDLE generalizes without subject-specific tuning to simulated source estimation, intracranial stimulation localization, and epileptogenic zone estimation.
Null-space learning
The model learns only the source component that cannot be directly recovered from EEG.
Zero-shot transfer
A simulator-trained prior transfers to empirical EEG without tuning on each subject.
Method
Learn only the unobservable component.
Given EEG signals and a subject-specific lead-field matrix, CANDLE denoises the measurements, analytically reconstructs the range-space component, and estimates the hidden null-space component with a temporal model.
ObservableL† Xdenoise
+
Analytic range-space recovery
UnobservableLn gγ(L† Xdenoise)
=
Learned null-space prior
EstimateŶ
Geometry-consistent source
Simulator
Neurobiologically grounded training data.
Because ground-truth cortical activity cannot be observed in real recordings, we construct a whole-brain simulator that combines subject-specific anatomy, neural mass dynamics, structural connectivity, and cognitive source patterns.
1,113subject-specific geometries
26,273statistical brain maps
994cortical source regions
5–20 dBsimulated EEG SNR
Results
Three complementary evaluations.
CANDLE is evaluated from fully controlled simulation to two empirical clinical settings. Learning-based methods are trained only on simulated data.
01
Simulated source activity
Subject-held-out evaluation across unseen cortical geometries. CANDLE recovers more localized sources and more faithful temporal dynamics than seven representative ESI baselines.
37.3 mmHD95 ↓
0.48Dice ↑
02
Intracranial stimulation localization
Zero-shot sim-to-real evaluation on 291 stimulation runs from 32 patients. CANDLE remains comparatively robust as stimulation sites become deeper.
54.1 mmSpatial dispersion ↓
32.9 mmPeak distance ↓
03
Epileptogenic zone estimation
Clinical evaluation on presurgical interictal EEG from 22 patients, using the postsurgical resection cavity as a reference for the epileptogenic zone.
61.7 mmHD95 ↓
35.4 mmCentroid distance ↓
Ablation
Each component contributes.
Removing the null-space estimator, training objectives, anatomical diversity, or neurobiologically grounded source definitions degrades performance across the empirical tasks.
Availability
Resources will follow the review timeline.
The manuscript link will be added after the arXiv submission. Source code will be released after acceptance.
PaperarXiv · coming soon
CodeRelease after acceptance