Weighted Structured Errors-in-Variables Methods for Noise-Robust Coherence Analysis

Abstract

Coherence analysis is commonly used to assess the frequency-dependent correlation between two time series in a wide range of disciplines, including neuroscience, astronomy, and acoustic engineering. However, its effectiveness can be substantially degraded by measurement noise, especially when both signals are contaminated. This paper proposes a weighted structured errors-in-variables (WSEIV) framework for noise-robust coherence estimation, formulated as a synchronous-component recovery problem under measurement uncertainty. Within this framework, four estimators — total least squares, weighted total least squares, structured total least squares, and weighted structured total least squares — are assessed to recover noise-reduced representations of synchronous components for improved coherence estimation. The latter three formulations explicitly account for unequal noise variances and structural constraints in the data matrix, either independently or jointly. The proposed framework is validated using synthetic signals across a range of signal-to-noise ratios and further evaluated in a representative corticomuscular coupling application using electroencephalogram and electromyogram recordings. Results demonstrate that the WSEIV methods consistently enhance coherence estimation under noisy conditions, improving the recovery of coupling-related signal components from contaminated measurements. This methodology provides a generalizable framework for frequency-resolved coupling analysis in situations where connectivity must be inferred from noisy measurements.