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.

Anonymous authors · Double-blind review

Explore the method Paper · arXiv soon Code · after acceptance
Overview of the CANDLE source imaging framework
CANDLE decomposes cortical source activity into an observable range-space component and a learned null-space component.

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.

01

Geometry-aware

A lead-field matrix derived from each subject's T1-weighted MRI constrains the source estimate.

02

Null-space learning

The model learns only the source component that cannot be directly recovered from EEG.

03

Zero-shot transfer

A simulator-trained prior transfers to empirical EEG without tuning on each subject.

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

Detailed architecture of CANDLE
Method overview. The subject-specific anatomical constraint is preserved throughout range–null space decomposition.

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.

Whole-brain simulator used to train CANDLE
Whole-brain simulation across 1,113 cortical geometries, with source configurations derived from 26,273 statistical brain maps.
1,113subject-specific geometries
26,273statistical brain maps
994cortical source regions
5–20 dBsimulated EEG SNR

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 ↑
Results for simulated cortical source activity estimation
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 ↓
Results for intracranial stimulation localization
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 ↓
Results for epileptogenic zone estimation

Each component contributes.

Removing the null-space estimator, training objectives, anatomical diversity, or neurobiologically grounded source definitions degrades performance across the empirical tasks.

Ablation results for the CANDLE architecture, loss, and simulator

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