Initial commit
This commit is contained in:
redclawsystems
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//! Signal Space Projection (SSP) for artifact removal.
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//!
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//! SSP is a spatial filtering technique that removes artifacts by projecting
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//! out directions in sensor space that contain artifact activity.
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//!
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//! ## Mathematical Background
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//!
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//! Given artifact data matrix A [n_channels x n_samples], we compute the
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//! covariance C = A * A^T and find its principal components via SVD.
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//!
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//! The projection operator is: P = I - Σ(u_i * u_i^T)
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//! where u_i are the artifact subspace vectors to remove.
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//!
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//! Clean data is obtained by: M_clean = P * M
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use crate::{SignalError, SignalResult};
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/// SSP projector for artifact removal
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#[derive(Debug, Clone)]
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pub struct SspProjector {
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/// Projection vectors [n_projectors x n_channels]
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/// Each row is a unit vector defining an artifact direction
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vectors: Vec<Vec<f64>>,
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/// Whether each projector is active
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active: Vec<bool>,
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/// Explained variance by each projector
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explained_var: Vec<f64>,
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/// Names/descriptions of projectors
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names: Vec<String>,
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/// Number of channels
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n_channels: usize,
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}
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impl SspProjector {
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/// Create an SSP projector from artifact epochs
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///
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/// # Arguments
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/// * `epochs` - Artifact epochs [n_epochs][n_channels][n_samples]
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/// * `n_components` - Number of projectors to compute
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/// * `name` - Name for this projector set (e.g., "EOG", "ECG")
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///
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/// # Returns
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/// SSP projector with the requested number of components
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pub fn from_epochs(
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epochs: &[Vec<Vec<f64>>],
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n_components: usize,
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name: &str,
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) -> SignalResult<Self> {
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if epochs.is_empty() {
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return Err(SignalError::InvalidLength("No epochs provided".to_string()));
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}
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let n_channels = epochs[0].len();
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if n_channels == 0 {
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return Err(SignalError::InvalidLength("Empty channels".to_string()));
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}
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// Concatenate all epochs into a data matrix [n_channels x total_samples]
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let total_samples: usize = epochs.iter().map(|e| e[0].len()).sum();
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let mut data = vec![vec![0.0; total_samples]; n_channels];
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let mut offset = 0;
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for epoch in epochs {
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let n_times = epoch[0].len();
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for ch in 0..n_channels {
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for t in 0..n_times {
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data[ch][offset + t] = epoch[ch][t];
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}
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}
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offset += n_times;
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}
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// Compute covariance matrix: C = (1/n) * X * X^T
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let mut cov = vec![vec![0.0; n_channels]; n_channels];
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for i in 0..n_channels {
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for j in i..n_channels {
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let mut sum = 0.0;
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for t in 0..total_samples {
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sum += data[i][t] * data[j][t];
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}
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cov[i][j] = sum / total_samples as f64;
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cov[j][i] = cov[i][j];
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}
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}
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// Compute SVD of covariance matrix
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let (eigenvectors, eigenvalues) = symmetric_eigen(&cov)?;
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// Total variance
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let total_var: f64 = eigenvalues.iter().sum();
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// Extract top n_components
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let n_proj = n_components.min(n_channels);
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let mut vectors = Vec::with_capacity(n_proj);
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let mut explained_var = Vec::with_capacity(n_proj);
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let mut names = Vec::with_capacity(n_proj);
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let mut active = Vec::with_capacity(n_proj);
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for i in 0..n_proj {
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vectors.push(eigenvectors[i].clone());
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explained_var.push(eigenvalues[i] / total_var);
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names.push(format!("{}-{}", name, i + 1));
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active.push(true);
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}
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Ok(Self {
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vectors,
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active,
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explained_var,
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names,
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n_channels,
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})
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}
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/// Create SSP projector from EOG data
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///
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/// # Arguments
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/// * `data` - Continuous data [n_channels][n_samples]
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/// * `eog_channels` - Indices of EOG channels
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/// * `n_components` - Number of projectors (typically 1-2)
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pub fn from_eog(
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data: &[Vec<f64>],
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eog_channels: &[usize],
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n_components: usize,
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) -> SignalResult<Self> {
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if data.is_empty() {
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return Err(SignalError::InvalidLength("Empty data".to_string()));
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}
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let n_channels = data.len();
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let n_samples = data[0].len();
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// Create artifact epochs from EOG threshold crossings
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let mut artifact_epochs = Vec::new();
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for &eog_ch in eog_channels {
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if eog_ch >= n_channels {
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return Err(SignalError::InvalidParameters(format!(
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"EOG channel {eog_ch} out of range"
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)));
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}
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// Find threshold (use robust estimate: 5 * median absolute deviation)
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let eog_data = &data[eog_ch];
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let threshold = compute_robust_threshold(eog_data);
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// Find peaks above threshold
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let peaks = find_peaks(eog_data, threshold);
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// Extract epochs around each peak (±100 samples or available)
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let half_window = 100.min(n_samples / 2);
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for peak in peaks {
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let start = peak.saturating_sub(half_window);
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let end = (peak + half_window).min(n_samples);
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let epoch: Vec<Vec<f64>> = data.iter().map(|ch| ch[start..end].to_vec()).collect();
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artifact_epochs.push(epoch);
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}
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}
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if artifact_epochs.is_empty() {
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// Create a projector from the raw EOG channel correlation
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return Self::from_eog_correlation(data, eog_channels, n_components);
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}
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Self::from_epochs(&artifact_epochs, n_components, "EOG")
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}
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/// Create SSP from EOG channel correlation (fallback method)
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fn from_eog_correlation(
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data: &[Vec<f64>],
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eog_channels: &[usize],
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n_components: usize,
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) -> SignalResult<Self> {
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let n_channels = data.len();
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let n_samples = data[0].len();
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// Compute correlation of each channel with EOG channels
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let mut vectors = Vec::new();
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let mut explained_var = Vec::new();
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for (comp_idx, &eog_ch) in eog_channels.iter().take(n_components).enumerate() {
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let eog_data = &data[eog_ch];
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let eog_var: f64 = eog_data.iter().map(|&x| x * x).sum::<f64>() / n_samples as f64;
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if eog_var < 1e-15 {
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continue;
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}
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// Compute correlation vector
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let mut corr_vec = vec![0.0; n_channels];
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for ch in 0..n_channels {
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let cov: f64 = (0..n_samples)
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.map(|t| data[ch][t] * eog_data[t])
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.sum::<f64>()
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/ n_samples as f64;
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corr_vec[ch] = cov / eog_var.sqrt();
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}
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// Normalize
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let norm: f64 = corr_vec.iter().map(|&x| x * x).sum::<f64>().sqrt();
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if norm > 1e-10 {
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for v in &mut corr_vec {
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*v /= norm;
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}
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vectors.push(corr_vec);
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explained_var.push(1.0 / (comp_idx + 1) as f64);
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}
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}
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let n_proj = vectors.len();
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Ok(Self {
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vectors,
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active: vec![true; n_proj],
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explained_var,
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names: (0..n_proj).map(|i| format!("EOG-{}", i + 1)).collect(),
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n_channels,
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})
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}
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/// Create SSP projector from ECG data
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///
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/// # Arguments
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/// * `data` - Continuous data [n_channels][n_samples]
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/// * `ecg_channel` - Index of ECG channel
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/// * `n_components` - Number of projectors (typically 1-3)
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pub fn from_ecg(
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data: &[Vec<f64>],
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ecg_channel: usize,
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n_components: usize,
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) -> SignalResult<Self> {
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if data.is_empty() {
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return Err(SignalError::InvalidLength("Empty data".to_string()));
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}
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let n_channels = data.len();
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let n_samples = data[0].len();
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if ecg_channel >= n_channels {
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return Err(SignalError::InvalidParameters(format!(
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"ECG channel {ecg_channel} out of range"
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)));
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}
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let ecg_data = &data[ecg_channel];
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// Find R-peaks using simple threshold detection
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let threshold = compute_robust_threshold(ecg_data);
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let r_peaks = find_peaks(ecg_data, threshold);
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if r_peaks.len() < 3 {
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return Err(SignalError::InvalidLength(
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"Not enough ECG peaks detected".to_string(),
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));
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}
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// Extract epochs around each R-peak (±50 samples)
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let half_window = 50.min(n_samples / 2);
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let mut artifact_epochs = Vec::new();
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for peak in r_peaks {
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let start = peak.saturating_sub(half_window);
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let end = (peak + half_window).min(n_samples);
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let epoch: Vec<Vec<f64>> = data.iter().map(|ch| ch[start..end].to_vec()).collect();
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artifact_epochs.push(epoch);
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}
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Self::from_epochs(&artifact_epochs, n_components, "ECG")
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}
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/// Apply the SSP projector to data
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///
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/// # Arguments
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/// * `data` - Data to clean [n_channels][n_samples]
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///
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/// # Returns
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/// Cleaned data with artifacts removed
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pub fn apply(&self, data: &[Vec<f64>]) -> SignalResult<Vec<Vec<f64>>> {
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if data.len() != self.n_channels {
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return Err(SignalError::InvalidLength(format!(
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"Expected {} channels, got {}",
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self.n_channels,
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data.len()
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)));
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}
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let n_samples = data[0].len();
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// Compute projection matrix: P = I - Σ(u_i * u_i^T)
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// For efficiency, we apply it directly: y = x - Σ((u_i^T * x) * u_i)
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let mut result = data.to_vec();
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for (i, vec) in self.vectors.iter().enumerate() {
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if !self.active[i] {
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continue;
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}
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for t in 0..n_samples {
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// Compute dot product: u^T * x
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let dot: f64 = (0..self.n_channels).map(|ch| vec[ch] * data[ch][t]).sum();
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// Subtract: x = x - (u^T * x) * u
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for ch in 0..self.n_channels {
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result[ch][t] -= dot * vec[ch];
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}
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}
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}
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Ok(result)
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}
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/// Apply SSP to epoched data
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///
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/// # Arguments
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/// * `epochs` - Epoched data [n_epochs][n_channels][n_samples]
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///
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/// # Returns
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/// Cleaned epochs
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pub fn apply_epochs(&self, epochs: &[Vec<Vec<f64>>]) -> SignalResult<Vec<Vec<Vec<f64>>>> {
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epochs.iter().map(|epoch| self.apply(epoch)).collect()
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}
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/// Activate or deactivate a projector
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pub fn set_active(&mut self, index: usize, active: bool) -> SignalResult<()> {
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if index >= self.vectors.len() {
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return Err(SignalError::InvalidParameters(format!(
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"Projector index {index} out of range"
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)));
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}
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self.active[index] = active;
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Ok(())
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}
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/// Get number of projectors
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pub fn n_projectors(&self) -> usize {
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self.vectors.len()
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}
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/// Get number of active projectors
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pub fn n_active(&self) -> usize {
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self.active.iter().filter(|&&a| a).count()
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}
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/// Get projector vectors
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pub fn vectors(&self) -> &[Vec<f64>] {
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&self.vectors
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}
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/// Get explained variance ratios
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pub fn explained_var(&self) -> &[f64] {
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&self.explained_var
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}
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/// Get projector names
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pub fn names(&self) -> &[String] {
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&self.names
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}
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/// Check if projector is active
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pub fn is_active(&self, index: usize) -> bool {
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self.active.get(index).copied().unwrap_or(false)
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}
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/// Compute the projection matrix P = I - Σ(u_i * u_i^T)
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pub fn compute_projection_matrix(&self) -> Vec<Vec<f64>> {
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let n = self.n_channels;
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let mut proj = vec![vec![0.0; n]; n];
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// Start with identity
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for i in 0..n {
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proj[i][i] = 1.0;
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}
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// Subtract outer products of active projectors
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for (i, vec) in self.vectors.iter().enumerate() {
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if !self.active[i] {
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continue;
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}
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for row in 0..n {
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for col in 0..n {
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proj[row][col] -= vec[row] * vec[col];
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}
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}
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}
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proj
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}
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/// Merge multiple SSP projectors
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pub fn merge(projectors: &[&SspProjector]) -> SignalResult<Self> {
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if projectors.is_empty() {
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return Err(SignalError::InvalidParameters(
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"No projectors to merge".to_string(),
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));
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}
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let n_channels = projectors[0].n_channels;
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for p in projectors {
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if p.n_channels != n_channels {
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return Err(SignalError::InvalidParameters(
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"Channel count mismatch".to_string(),
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));
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}
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}
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let mut vectors = Vec::new();
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let mut active = Vec::new();
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let mut explained_var = Vec::new();
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let mut names = Vec::new();
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for p in projectors {
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vectors.extend(p.vectors.clone());
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active.extend(p.active.clone());
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explained_var.extend(p.explained_var.clone());
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names.extend(p.names.clone());
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}
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Ok(Self {
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vectors,
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active,
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explained_var,
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names,
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n_channels,
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})
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}
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}
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/// Compute robust threshold using median absolute deviation
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fn compute_robust_threshold(data: &[f64]) -> f64 {
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let mut sorted: Vec<f64> = data.iter().map(|&x| x.abs()).collect();
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sorted.sort_by(|a, b| a.partial_cmp(b).unwrap());
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let median = if sorted.len().is_multiple_of(2) {
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f64::midpoint(sorted[sorted.len() / 2 - 1], sorted[sorted.len() / 2])
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} else {
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sorted[sorted.len() / 2]
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};
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// MAD = median(|x - median|)
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let mut deviations: Vec<f64> = data.iter().map(|&x| (x.abs() - median).abs()).collect();
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deviations.sort_by(|a, b| a.partial_cmp(b).unwrap());
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let mad = if deviations.len().is_multiple_of(2) {
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f64::midpoint(deviations[deviations.len() / 2 - 1], deviations[deviations.len() / 2])
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} else {
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deviations[deviations.len() / 2]
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};
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// 5 * MAD is a robust threshold
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5.0 * mad.max(1e-10)
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}
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/// Find peaks above threshold with minimum separation
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fn find_peaks(data: &[f64], threshold: f64) -> Vec<usize> {
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let min_separation = 50; // Minimum samples between peaks
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let mut peaks = Vec::new();
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let mut last_peak: Option<usize> = None;
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for i in 1..data.len().saturating_sub(1) {
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if data[i] > threshold && data[i] > data[i - 1] && data[i] > data[i + 1] {
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if let Some(last) = last_peak {
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if i - last >= min_separation {
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peaks.push(i);
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last_peak = Some(i);
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}
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} else {
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peaks.push(i);
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last_peak = Some(i);
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}
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}
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}
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peaks
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}
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/// Compute eigendecomposition of symmetric matrix using power iteration
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fn symmetric_eigen(matrix: &[Vec<f64>]) -> SignalResult<(Vec<Vec<f64>>, Vec<f64>)> {
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let n = matrix.len();
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if n == 0 {
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return Ok((vec![], vec![]));
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}
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let mut eigenvectors = Vec::with_capacity(n);
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let mut eigenvalues = Vec::with_capacity(n);
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let mut work_matrix = matrix.to_vec();
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for _ in 0..n {
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// Power iteration to find largest eigenvalue/vector
|
||||
let (eigval, eigvec) = power_iteration(&work_matrix, 100)?;
|
||||
|
||||
if eigval.abs() < 1e-15 {
|
||||
break;
|
||||
}
|
||||
|
||||
eigenvalues.push(eigval);
|
||||
eigenvectors.push(eigvec.clone());
|
||||
|
||||
// Deflate: A = A - λ * v * v^T
|
||||
for i in 0..n {
|
||||
for j in 0..n {
|
||||
work_matrix[i][j] -= eigval * eigvec[i] * eigvec[j];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
Ok((eigenvectors, eigenvalues))
|
||||
}
|
||||
|
||||
/// Power iteration to find dominant eigenvalue/vector
|
||||
fn power_iteration(matrix: &[Vec<f64>], max_iter: usize) -> SignalResult<(f64, Vec<f64>)> {
|
||||
let n = matrix.len();
|
||||
if n == 0 {
|
||||
return Err(SignalError::InvalidLength("Empty matrix".to_string()));
|
||||
}
|
||||
|
||||
// Initialize with random-ish vector
|
||||
let mut v: Vec<f64> = (0..n).map(|i| ((i + 1) as f64).sin()).collect();
|
||||
|
||||
// Normalize
|
||||
let mut norm: f64 = v.iter().map(|&x| x * x).sum::<f64>().sqrt();
|
||||
for x in &mut v {
|
||||
*x /= norm;
|
||||
}
|
||||
|
||||
let mut eigenvalue = 0.0;
|
||||
|
||||
for _ in 0..max_iter {
|
||||
// w = A * v
|
||||
let w: Vec<f64> = (0..n)
|
||||
.map(|i| (0..n).map(|j| matrix[i][j] * v[j]).sum())
|
||||
.collect();
|
||||
|
||||
// Rayleigh quotient: λ = v^T * A * v
|
||||
eigenvalue = (0..n).map(|i| v[i] * w[i]).sum();
|
||||
|
||||
// Normalize w
|
||||
norm = w.iter().map(|&x| x * x).sum::<f64>().sqrt();
|
||||
if norm < 1e-15 {
|
||||
break;
|
||||
}
|
||||
|
||||
// Check convergence
|
||||
let diff: f64 = (0..n).map(|i| (w[i] / norm - v[i]).abs()).sum::<f64>();
|
||||
|
||||
v = w.iter().map(|&x| x / norm).collect();
|
||||
|
||||
if diff < 1e-10 {
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
Ok((eigenvalue, v))
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use super::*;
|
||||
|
||||
#[test]
|
||||
fn test_ssp_from_epochs() {
|
||||
// Create simple artifact epochs
|
||||
let epochs = vec![
|
||||
vec![
|
||||
vec![1.0, 2.0, 3.0, 2.0, 1.0],
|
||||
vec![0.5, 1.0, 1.5, 1.0, 0.5],
|
||||
vec![0.2, 0.4, 0.6, 0.4, 0.2],
|
||||
],
|
||||
vec![
|
||||
vec![1.1, 2.1, 3.1, 2.1, 1.1],
|
||||
vec![0.55, 1.05, 1.55, 1.05, 0.55],
|
||||
vec![0.22, 0.42, 0.62, 0.42, 0.22],
|
||||
],
|
||||
];
|
||||
|
||||
let ssp = SspProjector::from_epochs(&epochs, 2, "test").unwrap();
|
||||
|
||||
assert!(ssp.n_projectors() >= 1);
|
||||
assert_eq!(ssp.n_active(), ssp.n_projectors());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_ssp_apply() {
|
||||
// Create a known projector
|
||||
let ssp = SspProjector {
|
||||
vectors: vec![vec![1.0, 0.0, 0.0]], // Project out first channel
|
||||
active: vec![true],
|
||||
explained_var: vec![0.5],
|
||||
names: vec!["test-1".to_string()],
|
||||
n_channels: 3,
|
||||
};
|
||||
|
||||
let data = vec![
|
||||
vec![1.0, 2.0, 3.0],
|
||||
vec![4.0, 5.0, 6.0],
|
||||
vec![7.0, 8.0, 9.0],
|
||||
];
|
||||
|
||||
let cleaned = ssp.apply(&data).unwrap();
|
||||
|
||||
// First channel should be zeroed
|
||||
assert!(cleaned[0].iter().all(|&x| x.abs() < 1e-10));
|
||||
// Other channels unchanged
|
||||
assert_eq!(cleaned[1], vec![4.0, 5.0, 6.0]);
|
||||
assert_eq!(cleaned[2], vec![7.0, 8.0, 9.0]);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_ssp_projection_matrix() {
|
||||
let ssp = SspProjector {
|
||||
vectors: vec![vec![1.0, 0.0], vec![0.0, 1.0]],
|
||||
active: vec![true, false],
|
||||
explained_var: vec![0.5, 0.3],
|
||||
names: vec!["p1".to_string(), "p2".to_string()],
|
||||
n_channels: 2,
|
||||
};
|
||||
|
||||
let proj = ssp.compute_projection_matrix();
|
||||
|
||||
// Only first projector is active, so P = I - u1*u1^T
|
||||
// u1 = [1, 0], so P = [[0, 0], [0, 1]]
|
||||
assert!((proj[0][0] - 0.0).abs() < 1e-10);
|
||||
assert!((proj[0][1] - 0.0).abs() < 1e-10);
|
||||
assert!((proj[1][0] - 0.0).abs() < 1e-10);
|
||||
assert!((proj[1][1] - 1.0).abs() < 1e-10);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_set_active() {
|
||||
let mut ssp = SspProjector {
|
||||
vectors: vec![vec![1.0, 0.0]],
|
||||
active: vec![true],
|
||||
explained_var: vec![0.5],
|
||||
names: vec!["p1".to_string()],
|
||||
n_channels: 2,
|
||||
};
|
||||
|
||||
assert!(ssp.is_active(0));
|
||||
ssp.set_active(0, false).unwrap();
|
||||
assert!(!ssp.is_active(0));
|
||||
assert_eq!(ssp.n_active(), 0);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_merge_projectors() {
|
||||
let p1 = SspProjector {
|
||||
vectors: vec![vec![1.0, 0.0, 0.0]],
|
||||
active: vec![true],
|
||||
explained_var: vec![0.5],
|
||||
names: vec!["EOG-1".to_string()],
|
||||
n_channels: 3,
|
||||
};
|
||||
|
||||
let p2 = SspProjector {
|
||||
vectors: vec![vec![0.0, 1.0, 0.0]],
|
||||
active: vec![true],
|
||||
explained_var: vec![0.3],
|
||||
names: vec!["ECG-1".to_string()],
|
||||
n_channels: 3,
|
||||
};
|
||||
|
||||
let merged = SspProjector::merge(&[&p1, &p2]).unwrap();
|
||||
|
||||
assert_eq!(merged.n_projectors(), 2);
|
||||
assert_eq!(merged.names()[0], "EOG-1");
|
||||
assert_eq!(merged.names()[1], "ECG-1");
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_power_iteration() {
|
||||
// Diagonal matrix - eigenvalues are diagonal elements
|
||||
let matrix = vec![vec![3.0, 0.0], vec![0.0, 1.0]];
|
||||
|
||||
let (eigval, eigvec) = power_iteration(&matrix, 100).unwrap();
|
||||
|
||||
// Largest eigenvalue should be 3
|
||||
assert!((eigval - 3.0).abs() < 1e-6);
|
||||
// Corresponding eigenvector should be [1, 0]
|
||||
assert!((eigvec[0].abs() - 1.0).abs() < 1e-6);
|
||||
assert!(eigvec[1].abs() < 1e-6);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_find_peaks() {
|
||||
let data = vec![0.0, 1.0, 5.0, 2.0, 0.0, 0.0, 0.0];
|
||||
let peaks = find_peaks(&data, 3.0);
|
||||
|
||||
assert_eq!(peaks.len(), 1);
|
||||
assert_eq!(peaks[0], 2);
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user