Study on Power Spectral Density by Improving Electroencephalography Signal Quality

An electroencephalogram is a recording of voltages at the scalp, and most of what it contains is not brain activity: muscle tension, eye blinks and mains interference all arrive on the same wires. The rhythm of interest here is the alpha band, 8–13 Hz, long established as a marker of relaxed wakefulness, which appears most strongly over the back of the head when a subject is resting with their eyes closed.

The question this project asks is whether the area under the alpha band of the power spectrum can serve as a usable quantitative index of restfulness — and, because that area is only as trustworthy as the signal it is computed from, whether a neural network trained to reconstruct clean traces from noisy ones can make the measurement more reliable. The two halves are inseparable: the denoising exists to make the integral mean something.

§Research question

Can the power in the alpha band of an EEG spectrum, measured as the area under the spectral curve, give a quantitative measure of cognitive stability or relaxation — and does machine-learning-based denoising of the raw recording improve that measurement?

§Theoretical background

An EEG trace is a voltage time series. Fourier analysis rewrites it as a superposition of sinusoids, so that a long and visually noisy recording can be summarised by how its power is distributed across frequency. The conventional bands are delta, theta, alpha, beta and gamma; the alpha band sits at 8–13 Hz.

Writing $x(t)$ for the recorded signal, the discrete Fourier transform gives coefficients

$$X_k = \sum_{n=0}^{N-1} x_n\, e^{-2\pi i k n / N},$$

from which the power spectrum $P(f) = |X(f)|^2$ follows. The quantity of interest is the band-limited integral

$$P_\alpha = \int_{8\,\mathrm{Hz}}^{13\,\mathrm{Hz}} P(f)\, \dd f,$$

evaluated numerically as the area under the spectral curve. Reported in units of $\mu\mathrm{V}^2$, this is the number the project treats as an index of restfulness, computed channel by channel so that its spatial distribution across the scalp can be compared.

Denoising is posed as a reconstruction problem. An autoencoder is trained to map a corrupted segment back to its clean counterpart by passing it through a narrow bottleneck, minimising the mean squared error

$$\mathcal{L} = \frac{1}{N}\sum_{n=1}^{N} \left( \hat{x}_n - x_n \right)^2 ,$$

so that the only way to reconstruct well is to learn the structure the signal has and the noise does not.

§Methodology

Acquisition. EEG was recorded from a subject on a 21-channel system placed according to the international 10–20 system, with conductive gel applied for signal quality and the participant instructed to minimise movement and external stimulation. The recorded REF data were converted to EDF for processing.

Preprocessing and noise injection. Signals were loaded in Python with pyedflib and normalised. Gaussian noise was then added artificially to the clean recordings, producing a paired dataset — clean and corrupted versions of the same segments — on which a denoiser could be trained supervised.

Denoising. An autoencoder was trained to separate neural signal from noise, with an encoder compressing the input and a decoder reconstructing it, on overlapping 256-sample segments, minimising mean squared error. The trained model was then applied to unseen segments.

Spectral analysis. Denoised signals were transformed to the frequency domain by FFT, the 8–13 Hz band isolated, and its power computed as the area under the spectral curve by trapezoidal integration (numpy.trapz). Alpha power was calculated per channel, with occipital and parietal channels of particular interest.

§Results and observations

Measured alpha power varied markedly across the scalp. The reported values were larger over the occipital and temporal channels — O1, O2, T5, T6 — than over frontal and central channels, which is the posterior-dominant distribution that alpha activity is expected to show during restful wakefulness.

One channel is given numerically: O1-AVG measured 2.2871 μV². The poster reports this as falling below a 20–50 μV² range described there as typical of relaxed healthy adults, and notes stress, cognitive activity, or occipital dysfunction among possible explanations. T6 and O2 are reported as showing higher alpha power than O1.

Denoising is reported as improving waveform clarity and the separability of neural signal from artefact, and the per-channel alpha measurements were combined into a topographic map so that spatial distribution and outlying channels could be inspected alongside the numbers.

§Challenges and limitations

• A single subject. All measurements come from one recording session on one participant. Nothing here supports a population claim, and the diagnostic possibilities the poster raises are speculation about an individual trace, not findings.
• The noise is synthetic. The autoencoder was trained on Gaussian noise added deliberately to clean recordings. Real EEG artefacts — blinks, EMG, electrode drift — are structured, non-Gaussian and correlated with the signal, so performance on this task does not establish performance on real artefacts.
• No quantified denoising benefit. Improvement in clarity is reported qualitatively. No reconstruction error, signal-to-noise ratio or before-and-after comparison of $P_\alpha$ is given.
• The reference range is uncited. The 20–50 μV² band the O1 value is compared against is stated without a source, and absolute alpha power depends strongly on montage, reference, epoch length and spectral normalisation — which makes any comparison against a literature range fragile.
• Internally inconsistent direction. The poster’s abstract describes the occipital channel O1 as showing the lowest alpha values while its results section describes O1 among the highest. The two cannot both be right; this page reports both the spatial pattern and the single numerical value without resolving the contradiction.