Broadband Frequency-Division Multiplexing in Visually Evoked
Potentials Enables Image Transmission and Physical Computing
Gao Wang, Maria Chiara Braidotti, Giulia Marcucci, Daniele Faccio
School of Physics & Astronomy, University of Glasgow, G12 8QQ Glasgow, UK

Steady-state visual evoked potentials (SSVEPs) are periodic signals in the EEG readout from thevisual cortex, generated when the eye perceives a periodically modulated light signal. Until now,SSVEPs have mainly been used in scenarios with a single or double light-modulation frequency. In
this study, we extend the concept of SSVEPs to multiple-frequency light modulation and demonstratethat the brain can simultaneously process hundreds of frequencies. At broad bandwidth, the higher
harmonics and nonlinear mixing between pairs of signals can overlap with the fundamental harmonics,
resulting in a complex EEG signal. We leverage this complexity to reconstruct images based on
frequency encoding and create an extreme learning machine capable of performing classification.

The steady-state visual evoked potential (SSVEP) is a phenomenon in which the brain responds
to a light signal that is modulated periodically in time, typically within the 3-30 Hz frequency range.
This can be detected using implanted electrodes or electroencephalography (EEG). So far, SSVEPs havemostly been studied using single or double light-modulation frequencies [1, 2], neglecting the potential
for more complex multiple-frequency excitation. Here, we demonstrate the feasibility of stimulating
SSVEPs with hundreds of frequencies using frequency-division multiplexing (FDM), resulting in highly
nonlinear mixing. We show that FDM generates sum and difference frequency terms that overlap with theinput modulation frequencies (i.e., fundamental harmonics), enabling the brain to function as a nonlinear
receiver, processor, or decoder with appropriate light signal design. By analyzing experimental data
statistically, we develop a brain model that simulates the input-output response to various light stimuli,
which is then used to generate synthetic data for training different machine learning (ML) architectures.
To create a broadband-frequency-encoded brain-computer interface (BCI), we train a deep neuralnetwork (DNN) to solve the inverse problem and reconstruct images. We encode each pixel of an image
into a different light-modulation frequency between 8 and 24 Hz, and then project the broadband FDM,
read as an SSVEP signal. Finally, the EEG signal is decoded back into an image using the DNN decoder.
As a proof of concept for the first extreme learning machine (ELM) utilizing SSVEPs, we use synthetic data to train a feedforward reservoir computing (RC) architecture for classification. We encode amultivariate numerical dataset using a narrowband FDM around 12 Hz and combine it with another narrowband FDM around 15 Hz to optimize linear regression through a genetic algorithm (GA). The overall
FDM serves as the ELM input layer, and the optimized linear regression performs the classification task.
Experimental Setup. The EEG device outlayer and a schematic overview of our set-up is shownin Fig. 1. In Fig. 1a, the SSVEP is detected by an EEG with the key electrode, Oz, placed at thecentral region of the visual cortex at the back of the head. We use a 3-pole EEG device, which has one
active electrode located in Oz (medial occipital electrode site) so as to collect SSVEP from the primaryvisual cortex. The EEG also has one reference electrode above the left ear, M1 position, and one groundelectrode above the right ear, M2 position.
(a)

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Figure 1: SSVEP Setup for BCI and RC. a) EEG device, b) BCI experiment, c) ELM architecture.
Figure 1b sketches out our BCI experiment. An image is encoded by FDM to include multiple
frequencies simultaneously. These signals are then combined and used to modulate the intensity of LEDlight. The participant wearing the EEG device observes the light projected onto a white wall, observing
a somewhat random flickering light instead of a periodically modulated image as in standard SSVEPexperiments. At the same time, the EEG response is collected to retrieve the image.

The input-reservoir-decoding architecture of ELM is shown in Fig. 1c. Here, the input FDM is split inx, encoding the multivariate numerical dataset attributes, and in α, control parameters chosen througha GA that optimize the decoding linear regression.
Broadband-Frequency-Encoded BCI. The experiment uses a reduced MNIST digital dataset ofhandwriting images of dimensions 16 × 16. To reduce the encoding complexity, instead of indexing theentire image pixel by pixel, each image is randomly indexed and divided into 16 strips. Each strip is thenencoded to modulate LED intensity for 16 trials. After completing all 16 trials, the transmission of one
complete image is achieved. At the same time, EEG responses are collected and fed into an EEG-to-ImageDNN for retrieving images. Figure 2a reports the ground truth digital handwriting images encoded intothe LED light. Reconstructed images obtained via the EEG-to-Image DNN decoder are shown in Fig. 2b.
(a)

(b)

Figure 2: BCI image retrieval. a) Ground truth images; b) Reconstructed images.

Reservoir Computing. Following our work on BCI, we show the first realization of an ELM bySSVEPs, where we exploit the brain nonlinearities to map the input stimuli into a high-dimensionalfeature domain. Using the same setup shown in Figs. 1a,b, we realize the ML architecture in Fig. 1c.
However, for ethical reasons, we chose not to expose the participant to an exhausting data collection for
the training of the network, preferring instead to use synthetic data.
In this experiment, the Breast cancer dataset [3] was divided into two parts: training data and testing
data. We used the training data along with control parameters optimized by GA. As shown in Fig. 1bby substituting images with multivariate series, we encode the testing data and control parameters as
narrowband stimuli in LED modulation around 12 and 15 Hz, respectively. Then, we collect EEG signals
to calculate their spectrum in the sum frequency generation interval.
The obtained results are presented in Fig. 3. The first row displays the spectrum, where red lines
are obtained employing our phenomenological nonlinear brain model, and black lines represent the true
EEG signal. In the second row, the classification probabilities, obtained by optimized linear regression,
are reported. We stress that here only the seventh spectrum is not correctly classified.

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Figure 3: Classification results. First row is the spectrum, with red lines theoretically derived, andblack lines obtained via EEG. Second row is the classification probability, where 0 stands for benign and1 stands for malignant. Only the seventh spectrum is not correctly classified.

References[1] A. M. Norcia, et al., J. Vision 15, 4 (2015).
[2] G. Wang and D. Faccio, Intell. Comput. 2, 0014 (2023).
[3] P. M. Murphy and D. W. Aha (1994), http://www.ics.uci.edu/ mlearn/MLRepository.html