Crate exg_source 

exg-source — EEG Source Localization in Pure Rust

Complete EEG source localization pipeline ported from MNE-Python, implemented in pure Rust with no C/BLAS dependencies. Uses faer for SVD and eigendecomposition.

This crate can be used standalone or as an optional dependency of exg (enabled by the default source feature).

End-to-end example

use exg_source::*;
use exg_source::covariance::Regularization;
use ndarray::Array2;

// 1. Define source space — 162 dipoles on a cortical sphere
let (src_pos, src_nn) = ico_source_space(2, 0.06, [0.0, 0.0, 0.04]);

// 2. Define electrode positions (e.g., from a 10-20 montage)
let n_elec = 32;
let electrodes = Array2::<f64>::zeros((n_elec, 3)); // your positions here

// 3. Compute forward model (3-shell spherical head)
let sphere = SphereModel::default(); // brain/skull/scalp
let fwd = make_sphere_forward(&electrodes, &src_pos, &src_nn, &sphere);

// 4. Estimate noise covariance from a baseline recording
let baseline = Array2::<f64>::zeros((n_elec, 5000));
let noise_cov = compute_covariance(&baseline, Regularization::ShrunkIdentity(None));

// 5. Build the inverse operator
let inv = make_inverse_operator(&fwd, &noise_cov, Some(0.8)).unwrap();

// 6. Apply to EEG data
let data = Array2::<f64>::zeros((n_elec, 1000));
let lambda2 = 1.0 / 9.0; // SNR² = 9
let stc = apply_inverse(&data, &inv, lambda2, InverseMethod::SLORETA).unwrap();

// 7. Assess solution quality
let (snr, snr_est) = estimate_snr(&data, &inv);
let r = make_resolution_matrix(&inv, &fwd, lambda2, InverseMethod::SLORETA).unwrap();
let errors = peak_localisation_error(&r);

Modules

Module	Description
source_space	Icosahedron and grid source space generation
forward	Spherical head model (Berg & Scherg) forward computation
covariance	Noise covariance estimation (empirical, Ledoit–Wolf, diagonal)
inverse	Inverse operator construction and application
eloreta	eLORETA iterative weight solver
resolution	Resolution matrix, PSF, CTF, and spatial metrics
snr	SNR estimation from whitened data
linalg	SVD, eigendecomposition, whitener (faer backend)

Inverse methods

Method	Noise-normalised?	Iterative?	Best for
MNE	✗	✗	Raw current density estimates
dSPM	✓	✗	Statistical maps, group studies
sLORETA	✓	✗	Localisation with low bias
eLORETA	✓	✓	Exact zero-bias localisation

Mathematical background

The whitened gain matrix is decomposed via SVD:

G_w = W @ G @ R^{1/2} = U @ S @ V^T

where W is the whitener (C_noise^{-1/2}), R is the source covariance (depth / orientation priors), and U, S, V are the SVD factors.

The inverse kernel is:

K = R^{1/2} @ V @ diag(s / (s² + λ²)) @ U^T @ W

Noise normalisation divides each source by its noise sensitivity:

• dSPM: norm_k = ‖V_k @ diag(reginv)‖
• sLORETA: norm_k = ‖V_k @ diag(reginv × √(1 + s²/λ²))‖
• eLORETA: iterative reweighting to achieve R = I (see eloreta)

Re-exports

pub use inverse::apply_inverse;

pub use inverse::apply_inverse_epochs;

pub use inverse::apply_inverse_epochs_full;

pub use inverse::apply_inverse_full;

pub use inverse::apply_inverse_with_options;

pub use inverse::make_inverse_operator;

pub use inverse::prepare_inverse;

pub use covariance::compute_covariance;

pub use covariance::compute_covariance_epochs;

pub use covariance::Regularization;

pub use resolution::get_cross_talk;

pub use resolution::get_point_spread;

pub use resolution::make_resolution_matrix;

pub use resolution::peak_localisation_error;

pub use resolution::relative_amplitude;

pub use resolution::spatial_spread;

pub use snr::estimate_snr;

pub use forward::make_sphere_forward;

pub use forward::make_sphere_forward_free;

pub use forward::SphereModel;

pub use source_space::grid_source_space;

pub use source_space::ico_n_vertices;

pub use source_space::ico_source_space;

Modules

covariance

Noise covariance estimation from sensor data.

eloreta

eLORETA (exact Low Resolution Electromagnetic Tomography) solver.

forward

Spherical forward model (EEG gain matrix computation).

inverse

Inverse operator construction and application.

linalg

Pure-Rust linear algebra helpers (SVD, eigendecomposition, whitener).

resolution

Resolution matrix computation.

snr

SNR estimation from sensor data and an inverse operator.

source_space

Source space generation.

Structs

EloretaOptions

Options for the eLORETA iterative solver.

ForwardOperator

Forward operator (gain matrix + metadata).

InverseOperator

Prepared inverse operator, ready for application to data.

NoiseCov

Noise covariance matrix.

SourceEstimate

Source-space estimate produced by apply_inverse.

Enums

InverseMethod

Choice of inverse method.

PickOri

How to handle source orientations in free-orientation inverse solutions.

SourceOrientation

Source orientation constraint.