- The paper introduces PEAP, leveraging autoregressive padding to mitigate filter-induced edge artifacts and bias in EEG phase estimation.
- PEAP achieved a median accuracy of 84.6% and outperformed four established methods by reducing systematic errors in phase estimation.
- The method is robust across diverse subject groups and signal qualities, offering practical benefits for closed-loop neurostimulation and clinical research.
Phase Estimation with Autoregressive Padding (PEAP): Mitigating Biases and Inaccuracies in EEG Phase Analysis
Introduction
Accurate estimation of the instantaneous phase of oscillatory brain signals is essential in both neuroscientific research and clinical neuroengineering applications, particularly EEG-triggered TMS protocols. Standard Hilbert-based methods are susceptible to edge artifacts induced by acausal bandpass filtering, which results in systematic bias and compromised accuracy at the end points of data segments. Despite various algorithmic attempts to correct or avoid these effects, robust unbiased estimation remains unresolved. This paper systematically identifies these deficiencies in established techniques and introduces Phase Estimation with Autoregressive Padding (PEAP), an alternative that leverages AR modeling to structurally resolve filter-induced artifacts without sacrificing signal integrity or interpretability (2604.02212).
Methodological Overview
Benchmarking and Datasets
The assessment comprises four prevalent estimation approaches: Phastimate, SSPE, ETP, and PhastPadding. Comparison is performed using a multi-cohort EEG dataset (n=72), including young and elderly controls, and stroke patients, ensuring methodological evaluation across signal quality and clinical conditions.
Data were carefully preprocessed: downsampled, detrended, Laplacian-referenced around motor hot spots, and finely epoched. Power spectra and SNRs for the 9–13 Hz mu-rhythm were computed to quantify signal quality. Phase ground truths were determined via acausal FIR filtering (order 230, 9–13 Hz) with Hilbert transform, following best practices.
Description of PEAP
PEAP circumvents traditional padding limitations by generating physiologically plausible forward signal extensions. Unlike reflect or zero-padding, it applies a high-order Burg AR model (order=130 in the optimal configuration, output padding ≈290 ms) on unfiltered data to forecast future samples, thereby physically shifting edge artifacts outside the estimation window. This avoids the need to interpolate or reconstruct post hoc as in Phastimate and ETP. Importantly, padding is done prior to any filtering, enhancing phase continuity and minimizing phase distortion.
Hyperparameters for all AR-based methods, including input epoch length and AR model selection, were rigorously optimized by grid search on a partitioned training set, employing circular RMSE and bias statistics. Multiple algorithms were re-tuned to minimize biases as evaluated by the Kuiper test on estimated phase distributions.
Statistical Analysis
Phase accuracy was defined as absolute normalized circular error. A linear mixed-effects model predicted estimation accuracy from method, dataset, and phase, with random effects accounting for subject-level dependencies in stroke cases. Main comparisons used Benjamini-Hochberg correction for multiple testing. Phase counts, conditional accuracy, and systematic bias were evaluated across phase bins, and SNR-accuracy dependencies were also analyzed.
Results
Superior Accuracy and Bias Reduction of PEAP
PEAP achieved the highest median accuracy (84.6%, MAD=17.4%) compared to PhastPadding, Phastimate, SSPE, and ETP. Accuracy improvements for instantaneous phase estimation over other methods ranged from 3.2% to 9.2%. Notably, only PEAP failed to show significant phase bias when tested via the circular Kuiper test—other methods systematically overestimated or underestimated certain phase bins (e.g., M-shaped overrepresentation of rising/falling phases in Phastimate and PhastPadding). PEAP also provided the most stable accuracy profile across phase bins, with minimal confidence intervals.
PEAP outperformed established methods in both continuous and forecasted phase estimation, with a clear decline in accuracy only for future samples and with decay rates comparable or superior to alternatives. Application in combination with ETP further enhanced predictive accuracy.
Robustness to Clinical and Signal Quality Variation
Differences in method accuracy did not vary between control and stroke datasets, supporting translational applicability. While phase estimation accuracy for all methods increased with higher SNR, bias levels remained uncorrelated with SNR, indicating that systematic errors are primarily methodological rather than data-dependent. The study's inclusion of rigorously acquired clinical data strengthens claims to generalizability.
Characterization of Systematic Errors
Established methods' inaccuracies are explained by:
- Filtering edge artifacts: Acausal filtering results in phase-clustering at segment ends, particularly around rising and falling transitions (due to the Gibbs phenomenon).
- Edge interpolation: Methods that cut segments to remove edges must interpolate, trading bias for increased random error as the cut grows.
- Model interpretability versus accuracy: Simpler methods (e.g., ETP) are more interpretable but inherently biased in non-sinusoidal or nonstationary data. More intricate (AR- and state-space) models, while somewhat less interpretable, provide more accurate and less biased estimation.
PEAP's strategy minimizes both sources of error without sacrificing interpretability, as the AR forecast can be inspected for physiological plausibility.
Implications and Future Directions
Practical Impacts
PEAP's superior bias profile ensures that phase-dependent analyses, such as closed-loop TMS-EEG or brain-state tracking, are more valid and comparable across studies and patient populations. The method substantially reduces artifactual phase clustering—improving the statistical validity of phase-dependent findings and ensuring methodological rigor in high-stakes clinical applications.
Theoretical Significance
By empirically decoupling systematic from random error in phase estimation, PEAP enables more precise investigation of oscillatory phase coding in neural data. It re-opens the possibility of rediscovering relationships previously obscured by methodological artifacts, allowing for recalibration of standards in the field.
Recommendations and Future Work
For analysis pipelines with additional pre-processing (e.g., high-pass filtering for ICA), the study recommends that padding be done prior to operations that might distort time-domain continuity. Future work should:
- Implement PEAP in real-time closed-loop systems
- Analyze PEAP’s performance with varying SNRs and non-ideal data
- Develop open-source toolboxes for flexible algorithm deployment and benchmarking
- Evaluate computational efficiency for time-critical applications
The potential exists for future consensus or hybrid methods, leveraging the strengths of various approaches tailored to specific research or clinical requirements.
Conclusion
This study demonstrates that established phase estimation methods in EEG analysis introduce significant and systematic biases, which threaten the validity of phase-dependent neuroscience and neuromodulation research. PEAP, through signal-adaptive autoregressive padding, provides a notable advance—yielding higher accuracy and near-zero bias, with robust applicability across populations and data quality. Adoption of PEAP will improve methodological transparency, reliability, and interpretability in both offline analysis and real-time phase-dependent neurostimulation (2604.02212).