The problem stems from a fundamental property of EEG. Electrodes do not measure absolute electrical potentials; they measure potential differences relative to a reference. Because no perfect, silent reference exists, researchers must choose one, and the choice shapes everything downstream. Previous work by the same group, based at the Universidad Autónoma del Estado de Morelos and the Universidad Nacional Autónoma de México, had already established that the median reference, in which each electrode’s signal is expressed relative to the median of all electrodes at every instant, produces functional brain networks that closely resemble those obtained from magnetoencephalography, a technique that is essentially reference-free. The median reference, it seemed, was the safest choice.

But EEG data also need to be filtered, typically into the classical frequency bands such as delta, theta, alpha, beta, and gamma, which are associated with different cognitive and physiological states. That raises a question that sounds almost trivial: should the signals be filtered first and then re-referenced to the median, a scheme the authors call FR, or re-referenced first and then filtered, a scheme they call RF? Intuition might favor RF, since re-referencing only once reduces the computational workload. The new study demonstrates that this shortcut comes at a steep and sometimes irreparable price.

The team, led by J. Daniel Arzate-Mena, Paola V. Olguín-Rodríguez, and Markus F. Müller, tested both schemes on three kinds of data: whole-night sleep EEG recordings from ten healthy young men, synthetic signals from controlled numerical models, and surrogate data that mimic the statistical properties of real EEG while containing no genuine correlations at all. The numerical models included Nf-Tori, which are linear superpositions of two thousand harmonic oscillations whose power spectra could be tuned to follow power laws of varying steepness, and IAAFT surrogates, which preserve the amplitude distribution and power spectrum of real recordings while destroying any true interdependence between channels. This combination allowed the researchers to know exactly what the correct answer should be, and to see precisely how each preprocessing scheme deviated from it.

The results were striking. When re-referencing was performed before filtering, the RF scheme, spurious positive cross-correlations appeared throughout the network, and they grew systematically stronger in the faster frequency bands. In the gamma band, during deep sleep, the average displacement of correlation values reached about 0.5, with individual estimates climbing as high as 0.75. The true spatial correlation structure was overshadowed by this flood of artificial correlations, simulating a kind of hypersynchronized brain dynamics that simply does not exist. In contrast, the FR scheme introduced only small, systematic negative shifts of roughly minus 0.025, which were not statistically significant.

Most alarming was the finding that the RF-induced artifacts are irreversible. The researchers applied a sophisticated statistical correction known as the Significant Average Correlation matrix, or SAC-matrix, which compares each pair of channels against surrogate data at a Bonferroni-corrected significance level to separate genuine correlations from random ones. For the FR scheme, this correction worked beautifully, essentially eliminating the tiny residual distortions. But for the RF scheme, even the SAC-matrix could not repair the damage. The artificial correlations survived the correction, meaning they become indistinguishable from genuine brain connectivity. Once the redundant information has been embedded into every channel by the flawed pipeline, no post-hoc statistical trick can tease it apart.

The mechanism behind the effect lies in the peculiar behavior of the median reference itself. At any given moment, the median of an odd number of channels equals the potential of one specific electrode, which is then subtracted from all the others. The researchers measured how long each electrode serves as the reference before another takes over. For steep power spectra, they found that high-amplitude, slow-frequency components can dominate the median signal for hundreds of consecutive sampling points. During these extended intervals, the same slow waveform is effectively stamped into every channel, embedding redundant information across the entire recording. When the data are subsequently filtered into fast frequency bands, the mismatch between the slow time scale of the reference signal and the fast time scale of the band creates the spurious correlations, with the effect most pronounced in the beta and gamma ranges.

The severity of the problem is governed by the power spectral exponent beta, the slope of the signal’s power spectrum. When the team tuned their synthetic signals to follow power laws from white noise, with beta equal to zero, up to steep red noise with beta equal to three, the artificial correlations grew with every increase in steepness. This matters because beta values of two or greater are not exotic. They characterize slow-wave sleep, the post-ictal period following focal epileptic seizures, anesthesia, neonatal recordings, and patients in vegetative states or coma. In the sleep data, the spectral slope correlated strongly with the amount of spurious gamma-band correlation under the RF scheme, with a correlation coefficient of roughly 0.85, while the FR scheme showed no such dependence. Deep sleep stages, with slopes approaching minus three, were hit hardest.

The implications reach well beyond sleep research. Any study that constructs functional brain networks from multivariate EEG recordings, whether investigating epilepsy, disorders of consciousness, infant development, or insomnia, could be producing distorted connectivity maps if the preprocessing order is wrong. The authors also showed that the global average reference, an alternative proposed back in 1950, suffers from its own flaw: high-amplitude channels dominate the average and induce spurious coupling in low-amplitude channels, a pattern that even the SAC-matrix cannot fully correct. The median reference, by contrast, is far more robust to amplitude differences caused by muscle or eye artifacts.

The team’s recommendation is clear: filter first, then re-reference, and always apply surrogate-corrected cross-correlations when analyzing signals with steep power spectra. The FR scheme demands more computation, since each filtered signal must be re-referenced individually, but the resulting distortions are an order of magnitude smaller and can be almost completely eliminated. Although the study was conducted on EEG, the authors emphasize that the principle applies to any multivariate recording in which spatial re-referencing and band-pass filtering are applied sequentially. In an era when brain connectivity studies inform everything from consciousness research to clinical diagnosis, the message is a sobering reminder that in signal processing, as in life, the order of operations is not a technical detail. It can be the difference between discovering how the brain truly communicates and chasing ghosts that the pipeline itself created.

Subject of Research: The effect of preprocessing step order on spurious correlations in EEG functional network analysis

Article Title: Irreversible functional network deformation induced by preprocessing scheme order in multivariate EEG recordings

Article References: Arzate-Mena, J. D., Olguín-Rodríguez, P. V., Corsi-Cabrera, M., López-Alvarado, E. A., & Müller, M. F. (2026). Irreversible functional network deformation induced by preprocessing scheme order in multivariate EEG recordings. Frontiers in Neuroinformatics, 20, Article 1907920. https://doi.org/10.3389/fninf.2026.1907920

Image Credits: AI Generated

DOI: 10.3389/fninf.2026.1907920

Keywords: EEG, preprocessing, functional connectivity, median reference, spurious correlations, spectral slope, sleep, surrogate data, cross-correlation, neuroinformatics, band-pass filtering, brain networks