Rapid-IAF: Rapid Identification of Individual Alpha Frequency in EEG Data Using Sequential Bayesian Estimation

Rapid and robust identification of the individual alpha frequency (IAF) in electroencephalogram (EEG) is an essential factor for successful brain-computer interface (BCI) use. Here we demonstrate an algorithm to determine the IAF from short-term resting-state scalp EEG data. First, we outlined the algorithm to determine IAF from short-term resting scalp EEG data and evaluated its reliability using a large-scale dataset of scalp EEG during motor imagery-based BCI use and independent dataset for generalizability confirmation (N = 147). Next, we characterized the relationship between IAF and responsive frequency band of sensorimotor rhythm, which exhibits prominent event-related desynchronization (SMR-ERD) while attempting unilateral and movement. The proposed sequential Bayesian estimation algorithm (Rapid-IAF) determined IAF from less than 26-second resting EEG data among 95% of participants, indicating a clear advance over the conventional methods, which uses 2–15 minutes of data in previous literatures. We confirmed that the determined IAF corresponded to the frequency of SMR, which exhibits the most prominent event-related desynchronization during BCI use (individual SMR-ERD frequency, ISF). Moreover, intraclass correlation revealed that the estimated IAF was more stable than ISF across sessions, suggesting its reliability and utility for robust BCI use without intermittent recalibration. In summary, our method rapidly and reliably determined IAF compared to the conventional method using the spectral power change based on task-related response. The method can be utilized to quick BCI initialization. The demonstration of rapid, task-free parametrization of individual variability of neural responses would be of importance for future BCI systems including neural communication via a cursor, an avatar or robots, and closed-loop neurofeedback training.

If IAF corresponds to ISF, the task-free, resting-state EEG data alone would be sufficient to capture the individual difference in ISF [21], [22].The conventional procedure to initialize a BCI by identifying ISF is in general time-consuming and burdensome since it requires test trials to acquire the taskrelated response.Meanwhile, an alternative procedure based on task-free, short-term resting-state EEG data is potentially useful for the plug-and-play of BCI.For clinical application of BCI in a real-world setup, it is of critical importance to rapidly initialize a BCI within the limited time, and to maintain motivation of patients, which could be impaired by repetitive calibration trials.However, the variability of IAF has been largely ignored when the peak detection algorithm was applied to the short-term data, impairing the reliability of identified frequency [23].
Here, to handle the variability of IAF and rapidly and reliably determine IAF from short-term resting EEG data, we propose an online IAF estimation algorithm, termed Rapid-IAF, using the sequential Bayesian estimation which iteratively calculates the parameters of probabilistic distributions behind the observed samples.We employed this method to estimate the IAF, stable during a 10-minute BCI session, from the variable samples of IAF identified from short-term EEG signals.The algorithm has been employed in the other fields of biosignal processing including scalp EEG to estimate the internal parameters from the limited acquired data [24], [25].Using a large-scale dataset of scalp EEG during motor imagery-based BCI use (N = 138, the total number of participants across four data collections) and open EEG dataset acquired by other research group, we tested whether the rapid, reliable, task-free IAF identification is possible by Rapid-IAF algorithm.Moreover, we characterized the efficacy and reliability of identified IAFs based on the pseudo-online BCI operation performance and the intraclass correlation coefficient as the metric for the inter-session reliability.

A. Sequential Bayesian Estimation of Individual Alpha Frequency
IAF exhibits individual differences in prominent frequencies [20] in spectral ranges [26] and in aperiodic component [23] due to aging.References [27] and [28], fluctuation of arousal [29] and attention [30], [31].Rapid-IAF algorithm herein aims to capture the average IAF from temporally variable samples of IAF while monitoring the convergence of IAF as the number of samples increase.To this end, we employed the sequential Bayesian estimation method to determine IAF from short-term resting state EEG signals.The main analysis was conducted for the EEG signals from C3 channel, where prominent SMR-ERD is found during the right finger movement attempt.Given that average power spectra calculated from the short-term data exhibits the fluctuation of IAF, we iteratively updated the 1-D Gaussian distribution by using Bayes' theorem as follows The graphical model is shown in Fig. 2A) [32].
As we assume the IAF samples identified from power spectra follow a normal distribution with mean Ī AF and variance σ , we used Bayes' theorem to estimate the parameters of distribution with unknown mean and variance.The prior probability density function was set as Normal-gamma distribution whose posterior probability also becomes the identical distribution.The probability density function with mean µ and precision (the inverse of variance) λ is described as follows: where N andGam represent the Gaussian and Gamma distribution, respectively, and m, β, a, b are the parameters to be estimated by the sequential Bayesian estimation.Specifically, we consider about µ, the conditional probability when the N samples of IAF represented by vector x were given, p (µ|λ, X) follows the gaussian distribution: x n +βm .Regarding the distribution of λ, it follows Gamma distribution: The posterior probability of the p (X) follows the student t-distribution: where µ s = m, λ s = β (1+β)b , ν s = 2a.Thus, the iterative calculation of the posterior probability using the acquired β, m, â and b as the prior of the following calculation (Fig. 2B).Using the sequential estimation protocol, the distribution of p (X) is estimated as shown in Fig. 2C.In this case, as the number of samples increased, the peak of probability distribution of IAF was converged around 11 Hz.
To distinguish the IAF identified from grand average data, hereafter the identified IAF using the algorithm was termed rapid-IAF.We applied the algorithm to IAF samples the power spectra derived from the 1-second resting EEG signals using fast Fourier Transform (STFT) with 90% overlap.Because the STFT analysis generates power spectral density (PSD) values every 100 ms, we used the moving averaged PSD using the latest 10 samples as one sample subjected to the Sequential Bayesian estimation algorithm.The IAF in each sample was identified after removing individually varied 1/f components using linear regression [33], [34].Then, the peak frequency between 8-13 Hz was identified as the IAF [35], [36].To compute IAF for grand average PSD data, we averaged all PSD samples during resting-state in a session and applied the IAF detection procedure above.The amount of resting-state EEG data in a session was different from data collections, at the least a 100-second resting EEG data was used for the grand average PSD calculation.
We extracted the samples of IAF from PSD of the latest EEG signals over SM1, and submitted to the sequential Bayesian estimation every 100 ms.We calculated the difference between the IAF determined from the grand average PSD and the rapid-IAF determined from the short-term resting EEG signals (0-100 s).

B. Dataset
Four scalp EEG data collections (N=138; N = 30, 30, 22 and 56, respectively) during resting and motor imagery tasks, measured by our research group, were analyzed in this study [37].All experiments were performed based on the Declaration of Helsinki and their protocols were by the Ethics Committee of the Faculty of Science and Technology, Keio University (IRB approval number: 2020-38 or 2021-74).The datasets are made public [38] while the original study in which dataset 1-3 were acquired is not published.All participants were instructed to exert kinesthetic motor imagery of right-hand extension with visual feedback of SMR-ERD derived from channels around contralateral SM1 (i.e., left hemisphere) [3], [11], [13], [39].
In all datasets, 128-channel scalp EEG was recorded with the same experiment setup.EEG signals were measured at 1000 Hz sampling rate, with electrodes positioned according to the international 10-10 electrode positions via the HydroCel Geodesic Sensor Net (EGI, Eugene, USA).The EEG signals were then amplified and digitized with the GES 400 (EGI, Eugene, USA).Cz channel was set as the reference channel.Preprocessing was conducted using EEGLAB toolbox.Reference [40] using MATLAB 2022a (The Mathworks, Inc, Massachusetts, USA).The standard bandpass filtering using FIR filters (linear phase type 1 FIR anti-aliasing filter) and a notch filter (50 Hz, a third-order Butterworth filter) were applied.Then, EEG signals were resampled to 128 Hz.
The first dataset (Experiment 1) consisted of EEG data from 30 participants (5 females, and 25 men).Participants underwent 8 sessions of motor imagery tasks on two consecutive days (i.e., 16 sessions).During motor imagery tasks participants were provided with the visual feedback of EEG-SMR ERD derived from channels around contralateral SM1 (i.e., left hemisphere).
The second dataset (Experiment 2) consisted of EEG data from 30 participants (2 females and 28 males).The procedure of SMR-ERD calculation for visual feedback was the identical with that employed in Experiment 1. However. 10 out of the 30 participants were provided no feedback of SMR-ERD throughout the experiment.In total, participants underwent 8 sessions of motor imagery tasks.
The third dataset (Experiment 3) consisted of EEG data from 22 participants (1 female and 21 males).Participants underwent 4 sessions of motor imagery tasks.In the four sessions, participants were not provided feedback of SMR-ERD.
The fourth dataset (Experiment 4) consisted of EEG data from 56 participants (7 females and 49 males).Participants underwent 5 sessions of motor imagery task.The dataset is the reanalysis of [41] and the detailed procedures were reported in the article.In addition, we analyzed EEG dataset from the other research group to further investigate the generalizability of the proposed algorithm.To this end, we analyzed BCI competition dataset IV 2a, containing resting-state and fourclass motor imagery data (right and left hand, foot and tongue movement) [42].This dataset consisted of EEG data from 9 participants.Participants underwent 6 sessions of motor imagery tasks.Participants were not provided feedback of SMR-ERD.

C. Spectral Power Profile Calculation
For the preprocessed EEG signals derived from the channel around the left SM1, used for the visual feedback of SMR-ERD (i.e., C3 channel, see also Dataset section), After the calculation of power spectra, SMR-ERD magnitude was quantified by the following formula: where R is the reference of averaged power and A is the power during the task period.
In addition, we calculated the signal-to-noise ratio (SNR) at the IAF using the following formula: where Power peak is the signal power of spectral peak calculated as the residual of the linear regression described above, and the Power 1/ f is the term of 1/f in the same model, fitted from the original PSD.

D. Characterization of Spatiospectral Similarity of Individually Adjusted EEG Frequency
While the main analysis was conducted for the EEG signals from C3 channel, topographic representation of SMR-ERD in the sensor-space, and statistically significant areas revealed by cortical source estimation were visualized using identical spectral power calculation procedures.To estimate cortical source distribution, Brainstorm toolbox [43] and sLoreta algorithm () [44] were employed.
For the grand average of SMR-ERD around 8-13 Hz, the frequency with the maximum of SMR-ERD magnitude was identified as ISF.Although the frequency identified by the procedure was termed by IAF in a couple of studies.References [45] and [46], we explicitly defined them as different frequencies, respectively.To test whether IAF and ISF correspond at the individual level, the session-by-session determined frequencies were averaged to calculate the representative frequency of individuals.Then, IAF and ISF were subjected to Spearman's correlation test.Since we defined ISF as the most responsive frequency during motor imagery task, for the foot and tongue motor imagery data included in the BCI competition dataset, we sought the frequency exhibiting prominent signal increase.

E. Intraclass Correlation Analysis
As described in section II-A, the characteristic frequencies for SMR components are variable due to the internal conditions of participants (e.g., fatigue, sleepiness).Therefore, the calibration based on any neural signal analysis, it is necessary to evaluate the stability of three frequencies identified by the different procedures (i.e., ISF, IAF, and rapid-IAF).We quantified the inter-session reliability was estimated using intraclass correlation coefficient (ICC).References [34] and [47].In particular, given that the number of sessions was different among the datasets, we calculated the reliability of each frequency by splitting results from each dataset.Note that the reliability is calculated using each participant as one sample (i.e., the reliability within the same participant across sessions was evaluated).

F. Pseudo-Online Analysis of SMR-ERD BCI Controllability
To quantify the utility of rapid frequency estimation using the proposed algorithm, we compared the controllability of BCI based on the pre-defined alpha-band (8-13 Hz), ISF, IAF and rapid-IAF.From each session, we extracted the time-frequency representation of the EEG signals from the contralateral SM1 (i.e., C3).Then, we calculated the band-power of four frequency bands by averaging the range of ± 1Hz.
The controllability of SMR-ERD based BCI was evaluated by the proportion of the successful detection of SMR-ERD during task period of each trial (i.e., the SMR-ERD more than 0% was observed).After the collection of each success rate, one-way ANOVA was applied to test the difference in the success rate across frequencies.

A. Efficacy of Sequential Bayesian Estimation of Individual Alpha Frequency
The efficacy of our algorithm, which estimates IAF from the short-term resting EEG data was tested using four datasets.Continuously recorded EEG signal data from a session (∼10 minutes across datasets) were firstly analyzed in the sessionby-session manner.Then, the IAF and ISF values from each session were averaged in a participant-wise manner.Results of rapid-IAF determination using the sequential Bayesian estimation.A: Group result of deviation from the grand average IAF as a function of time.B: Relationship between rapid-IAF and IAF identified from grand average power spectra.C: Relationship between rapid-IAF and individual SMR-ERD frequency (ISF).Fig. 4.
Results of rapid-IAF determination using the sequential Bayesian estimation for multi-class motor imagery data.A: Group result of deviation from the grand average IAF as a function of time.B: Relationship between rapid-IAF and IAF identified from grand average power spectra.C: Relationship between rapid-IAF and ISF.
The group-level result was shown in the Fig. 3A.At the group level, 26 seconds of resting-EEG signals were sufficient for the estimated IAF to correspond with those identified from all available data in 95% of participants (i.e., the mean ± 2 * standard deviation (SD) was less than 0.5 Hz).Likewise, the 99% of participants reach the convergence after 71 of seconds data acquisition.
After the determination of rapid-IAF (i.e., IAF determined from 26 s EEG data), we investigated its relationship with IAFs determined from grand average data from each participant as well as ISF.We analyzed the group-level consistency between rapid-IAF and IAF determined from the grand average data.A positive correlation was observed between the two frequencies (Fig. 3B, Spearman's correlation test: IAF, ρ = 0.68, p < 0.001).Their consistency was confirmed by the distribution of the difference between rapid-IAF and IAF (0.22 ± 0.9 Hz).We compared the results with the comparison between rapid-IAF and ISF (Fig. 3C, ρ = 0.52, p < 0.001).Results indicated comparable results with the relationship between IAF from grand average and ISF.
In addition, we evaluate the efficacy of the algorithm using a different collection of EEG dataset containing multi-class motor imagery data.The group-level result was shown in the Fig. 4A.At the group level, 21 seconds of resting-EEG signals were sufficient for the estimated IAF.Note that it was comparable with the results of main dataset using right-hand motor imagery data alone.The relationship between IAF determined with the algorithm (rapid-IAF) and IAF was consistent with the group-level relationship as observed in the main dataset (Fig. 4B, Spearman's correlation test: IAF, ρ = 0.90, p = 0.0023).The agreement between rapid-IAF and ISF was also in keeping with the main dataset (Fig. 4C, Spearman's correlation test: ISF, ρ = 0.64, p = 0.068) although the small number of participants resulted in the absence of statistical significance.

B. Relationship Between Individual Alpha and SMR-ERD Frequencies
To characterize the spatiospectral similarity of individually adjusted EEG frequency bands, we investigated the relationship between grand-average IAF and ISF.First, areas significantly activated during motor imagery period were visualized in both sensor-and source spaces (Fig. 5).These results indicate similar activation patterns yet focal activation around SM1 was observed in the IAF and ISF.
Second, we compared the absolute difference of frequency.IAFs and ISFs across participants were 10.60 ±1.3 Hz and 10.99 ± 1.3 Hz respectively, indicating the inter-participant variability influences the spectral power calculated with 1 Hz resolution.In keeping with this, the positive correlation between IAF and ISF was observed (Fig. 6A, Spearman's correlation test: ρ = 0.57, p < 0.001).As shown in Fig. 6B, the mean difference between IAF and ISF was -0.39±1.2Hz, suggesting the partial agreement between IAF and ISF.
Next, we tested if SMR-ERD calculation based on identified IAFs indicates a stronger magnitude than that based on the pre-defined alpha band (i.e., 8-13 Hz).As hypothesized, the calculated SMR-ERD magnitude was highly correlated and systematically stronger than that calculated from pre-defined alpha-band power (Fig. 6C, Pearson's correlation test: r = 0.82, p < 0.001; intercept of linear regression: 24.9, p < 0.001), suggesting the use of IAF for SMR-ERD calculation detects power attenuation more sensitively than that of alpha.Then, we tested the relationship between magnitude of spectral power peak, represented by SNR, and the voluntary controllability of SMR, represented by SMR-ERD magnitude at ISF.In keeping with previous findings in the studies on more general BCI control performance, there was a significantly positive correlation between SNR at IAF and SMR-ERD magnitude at ISF (Fig. 6D, Pearson's correlation test: r = 0.64, p < 0.001), suggesting the SMR-ERD magnitude of participants can be estimated without acquiring EEG data during tasks.
Finally, we compared the reliability of three frequencies: ISF, IAF, and rapid IAF using intraclass correlation coefficients.As shown in Table I, IAF and rapid IAF were more reliable than ISF, indicating less inter-session variability.
A supplementary movie (Supplementary movie 1) indicates the representative trial of BCI operation of a single participant.The y-axis indicates the SMR-ERD magnitude and x-axis indicates time.A success control indicates the cursor is kept in the red shaded areas.
Comparison of BCI controllability among frequencies used for features.The success rate was calculated based on the proportion of the successful detection of SMR-ERD during task period of each trial.One-way ANOVA and post-hoc t-tests with Bonferroni correction was conducted.A significantly lower success rate was found in the results of pre-defined alpha-band activity (conventional method) compared to the other three methods.While the ideal frequency method, that is ISF, indicated significantly higher success rate compared to IAF (determined using 3 min.resting-data) and rapid-IAF (determined using 26 seconds resting-data), The effect sizes exhibit the determination and ISF or IAF realizes the significant improvement on the BCI controllability.

IV. DISCUSSION
In this present study, we proposed an algorithm to rapidly identify IAF from short-term (26 s), task-free resting EEG data and successfully determined rapid-IAFs that corresponded with those of grand averages.The pseudo-online analysis revealed a significantly higher success rate using the rapid-IAF feature as the input of BCI compared to using pre-defined, fixed alpha-band, determined without calibration (Fig. 7).Moreover, the ISF, which requires EEG data during task period to be determined, corresponded to the rapid-IAF at the group-level (Fig. 3C).In the conventional SMR-based BCI experimental protocol, participants undergo a calibration session before using BCI use since neural decoders in BCI constructed with machine-learning algorithms are trained to fit the calibration data.This approach has used data during rehearsal of the BCI operation to identify ISF, that is the responsive frequency to detect SMR-ERD, while the alternative approach adopted here was the parameterization of individual SMR responsiveness from short-term resting EEG data by identifying IAF.In addition, the distribution of cortical sources and results of spectral analysis suggested that both frequencies were beneficial to detect sensorimotor activity compared to the pre-defined alpha-band.Thus, application of the proposed calibration algorithm, which only use resting-EEG data would contribute to the quick initialization of a BCI.
We demonstrated that our algorithm could identify IAF within 1 Hz frequency resolution, which is practically sufficient for BCI control since BCI classifiers use band power features averaged around 3 Hz [2], [11], [48].Because previous studies required at the least a 120-second resting EEG data for IAF detection [26], [33], the calibration time was around four times shorter, making it possible to achieve plug-andplay use of non-invasive BCIs using our task-free calibration procedure.We found the positive correlation between IAF and ISF and their correspondence at the level of 1 Hz frequency resolution.However, the standard deviation of differences between ISF and IAF was 1.2 Hz.The variability exceeding 1 Hz frequency resolution suggests that IAF and ISF do not have a one-to-one relationship albeit the SMR-ERD magnitude is calculated from the task-related power attenuation from reference signal power at rest.The inconsistency would be attributed to the broadband responses of SMR-ERD in some participants.While IAF can be specifically determined from the peak prominence of power spectra, ISFs are influenced by the responsiveness of SMR-ERD, which is more variable within and across participants [34], [49].ISF can be more variable than IAF within participants since the stronger ERD is associated with the broad modulation of spectral power at alpha-band [50].Hence, we posit IAF did not coincide with ISF despite SMR-ERD calculated based on IAF exhibited more prominent spectral changes than those based on predefined alpha-band.
The ICC analysis to test the inter-session reliability of three frequency types revealed the higher inter-session reliability of IAF compared to ISF.In particular, that of ISF in Exp. 3 indicated lower ICC which indicated modest reliability [51].It should be attributed to nature of the dataset, that is EEG signal acquisition under no visual feedback of SMR-ERD in Exp. 3.Because it has been reported the provision of neurofeedback reduces the variability of neural signals under control [52], other datasets indicated higher ICC in ISF.This finding suggests that the calibration session under no visual feedback does not achieve reliable parameterization of individual neural responses.On the contrary, the higher ICC of short-term IAF (ICC > 0.8 across four data collections) suggests its utility for the frequency determination in BCI calibration [51] yet future studies which systematically compare BCI controllability based on IAF and ISF during the online feedback system is warranted.
We posit that the proposed algorithm for rapid IAF determination is of potential utility for any other neural oscillations such as occipital alpha which reflects activities of visual cortices [35], [53], application of ECoG-based BCIs leveraging neural oscillatory features as decoder inputs [6], [8].Because alpha-band frequency reflects the cognitive processes for visual stimuli.References [35] and [53], the IAF determined for short-term EEG data can be utilized to monitor the variable neural responses to visual events.Because the conventional experiment protocol requires the long-term acquisition of resting state EEG to determine the stimulation parameters, the proposed algorithm can be utilized to change the parameters Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
online during or between stimulation presentations, enabling adaptive brain stimulation informed by real-time EEG monitoring [54].
The framework of sequential Bayesian estimation can be combined with other methods for parameterization of individual alpha frequency because the algorithm requires the time-resolved samples of IAF, which can be determined with other methods [23], [26].Using more reliable parameterization methods for the sequential input would enhance the reliability of determined rapid IAF.In summary, we used a large-scale dataset of EEG signals during motor imagery tasks to identify ISF-IAF relationships and proposed an algorithm to determine IAF from short-term resting EEG signals for better SMR-based BCI control.The method would contribute to the utility of non-invasive BCI in real-world use by omitting repetitive recalibration and by minimizing the calibration time without sacrificing the reliability of features targeted by BCI, and finally realize plug-and-play BCI operation.

V. CONCLUSION
In the present study, we demonstrated IAF can be identified from short-term (26 s) scalp EEG data using sequential Bayesian algorithm.Since the identified IAF corresponded to the responsive frequency of task-related power attenuation of scalp EEG (i.e., SMR-ERD), the results would support the calibration of neural decoders used in for BCIs and neurofeedback training.

CONFLICTS OF INTEREST
Junichi Ushiba is a founder and the representative director of the university startup company, Lifescapes Inc., involved in the research, development, and sales of rehabilitation devices, including brain-computer interfaces.He receives a salary from Lifescapes Inc., and holds shares in Lifescapes Inc.This company does not have any relationships with the device or setup used in the current study.The remaining author declare no competing interests.

Fig. 1 .
Fig. 1.Typical data of scalp EEG signals.A: An example of sensorimotor rhythm (SMR) and its event-related desynchronization (SMR-ERD) during right-hand motor imagery observed at C3. B: Power spectral density (PSD) during rest period.Resting-state SMR exhibits a prominent peak around 8-13 Hz, namely individual alpha frequency (IAF).C: PSD during task period.The frequency which exhibited most prominent SMR-ERD is termed as the individual SMR-ERD frequency (ISF).D: Topographic representation of SMR-ERD in ISF during motor imagery of right-finger movement.The sensorimotor cortex (SM1) contralateral hemisphere indicates SMR-ERD.

Fig. 2 .
Fig. 2. Sequential Bayesian estimation of individual alpha frequency.A: Schematic of graphical model.B: A representative result of sequential Bayesian estimation.The top and bottom panel indicate average and variance of estimated distribution, respectively.C: Changes in the Gaussian distribution.Lines colored by brighter green indicate the distribution more samples were used for estimation.

Fig. 3 .
Fig. 3.Results of rapid-IAF determination using the sequential Bayesian estimation.A: Group result of deviation from the grand average IAF as a function of time.B: Relationship between rapid-IAF and IAF identified from grand average power spectra.C: Relationship between rapid-IAF and individual SMR-ERD frequency (ISF).

Fig. 5 .
Fig. 5. Spatial characteristics of SMR-ERD in the four types of frequency bands.A: Topographic representation of SMR-ERD in the four types of frequency bands Top left: A topographic map of SMR-ERD in the predefined alpha-band during motor imagery.Top right: A topographic map of SMR-ERD in the individual SMR-ERD frequency during motor imagery (ideal case).Bottom left: A topographic map of SMR-ERD in the IAF during motor imagery.Bottom right: A topographic map of SMR-ERD in the rapid IAF during motor imagery (proposed).B: Cortical sources which exhibited significant spectral power change in the four types of frequency bands (all p < 0.05, F-test).Top left: Distributions of significant areas in the predefined alpha-band during motor imagery.Top right: Distributions of significant areas in the individual SMR-ERD frequency during motor imagery.Bottom left: Distributions of significant areas in the IAF during motor imagery.Bottom right: Distributions of significant areas in the rapid IAF during motor imagery.

Fig. 6 .
Fig. 6.Characterization of the relationship between individual alpha frequency (IAF) and event-related desynchronization of sensorimotor rhythm (SMR-ERD).A: Group-level relationship between IAF and ISF.B: Difference between IAF and ISF.C: Relationship between SMR-ERD magnitude at contralateral SM1 in IAF and those in the pre-defined alpha-band D: Relationship between signal-to-noise ratio of spectral peak at IAF and SMR-ERD magnitude at ISF, derived from contralateral SM1.

TABLE I INTRACLASS
CORRELATION OF FREQUENCY ESTIMATION METHODS Fig. 7. Results of BCI controllability comparison among SMR-features.