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Edited by: Peter Neri, University of Aberdeen, UK

Reviewed by: Giandomenico Iannetti, University of Oxford, UK; Thomas Charles Ferree, NeuroMetrix, Inc., USA

*Correspondence: Romain Grandchamp, Centre de Recherche Cerveau et Cognition, UMR5549, CNRS, Pavillon Baudot CHU Purpan, BP 25202, 31052 Toulouse Cedex, France. e-mail:

This article was submitted to Frontiers in Perception Science, a specialty of Frontiers in Psychology.

This is an open-access article subject to a non-exclusive license between the authors and Frontiers Media SA, which permits use, distribution and reproduction in other forums, provided the original authors and source are credited and other Frontiers conditions are complied with.

In electroencephalography, the classical event-related potential model often proves to be a limited method to study complex brain dynamics. For this reason, spectral techniques adapted from signal processing such as event-related spectral perturbation (ERSP) – and its variant event-related synchronization and event-related desynchronization – have been used over the past 20 years. They represent average spectral changes in response to a stimulus. These spectral methods do not have strong consensus for comparing pre- and post-stimulus activity. When computing ERSP, pre-stimulus baseline removal is usually performed after averaging the spectral estimate of multiple trials. Correcting the baseline of each single-trial prior to averaging spectral estimates is an alternative baseline correction method. However, we show that this method leads to positively skewed post-stimulus ERSP values. We eventually present new single-trial-based ERSP baseline correction methods that perform trial normalization or centering prior to applying classical baseline correction methods. We show that single-trial correction methods minimize the contribution of artifactual data trials with high-amplitude spectral estimates and are robust to outliers when performing statistical inference testing. We then characterize these methods in terms of their time–frequency responses and behavior compared to classical ERSP methods.

Electroencephalography and magnetoencephalography methods have become standard tools to study brain mechanisms. Different approaches have been used to unveil brain electrical activity in relation to sensory, motor, or cognitive events using electrical potential variations recorded either at the scalp level or from intra-cranial electrodes. The study of changes of the ongoing electroencephalogram (EEG) in response to stimulation started with event-related potentials (ERP) techniques, which relies on measuring the amplitude and latency of post-stimulus peaks in stimulus-locked EEG trial averages. The standard ERP model relies on the hypothesis that ERPs consist of stereotyped patterns of stimulus-locked electrical activity, superimposed onto an independent stationary stochastic EEG processes (Basar and Dumermuth,

The standard ERP model has been intensely debated for the past 10 years. In some rare cases, the standard ERP model may hold in particular for early pre-perceptual activity such as somatosensory evoked potentials with latencies as short as 20 ms (N20 wave; Yao and Dewald,

In the 1960s, while some researchers were starting to use ERPs, some other pioneer researchers were using pure-frequency based techniques to assess spontaneous EEG oscillatory changes under various conditions. Scientists compared the EEG spectrum of subjects with their eyes opened or their eyes closed, and observed an increased 10-Hz alpha power in the eyes-closed condition (Legewie et al.,

These new post-stimulus spectral estimation methods were called event-related desynchronization (ERD; Pfurtscheller and Aranibar,

Using ERSP is however not as simple as using ERP since there are a large number of variants. For example, it is possible to compute power using either fast Fourier transform (FFT) or Wavelet transforms (Delorme and Makeig,

In addition to using different spectral methods, ERSP variants may also use different baseline correction methods. When processing intra-cranial electrodes, researchers often avoid computing baselines and analyze raw time-varying spectral power variations (Tallon-Baudry et al.,

There are mainly two methods to perform baseline correction. These two methods rely on different assumptions about the EEG signal. The first method assumes an additive model where stimulus-induced power at specific frequencies adds onto existing power at these frequencies. The second alternative model consists in using a divisive baseline, which assumes an EEG gain model where the occurrence of a stimulus proportionally increases or decreases the amplitude of existing oscillatory EEG activity. Both models are widely used and, for the first time, we are comparing them in terms of their time–frequency response and behavior when performing statistical inference testing.

Finally, a new idea we are introducing here deals with trial-based baseline correction methods. The classical baseline approach involves first computing time–frequency decompositions for each trial, then computing a trial average, and as a last step removing the pre-stimulus baseline. However, as we show in this report, this method proves to be quite sensitive to noisy data trials. By contrast, it is also possible to perform different types of correction in single-trials prior to averaging time–frequency estimates. In this report, we compare new trial-based baseline correction approaches to classical baseline correction methods. We will demonstrate how our trial-based correction methods tend to make ERSP less sensitive to the presence of a limited number of trials with excessive ambient or physiological noise.

We will first describe the two different models used to compute ERSP for both the classical baseline correction approach and the single-trial baseline correction approach. We will then detail the two statistical methods implemented to compute significance. Finally, we will explain the procedure used to study ERSP robustness to noisy trials.

Two main methods for ERSP pre-stimulus baseline correction may be distinguished. We first present these two approaches, which for simplicity we have termed the ERSP “gain model” and the ERSP “additive model”. We describe how ERSPs are calculated for each of these models and then show how they can be adapted for single-trial baseline correction.

The event-related spectrum (ERS) consists in computing the data power spectrum for sliding time windows centered at time

where _{k}_{k}_{k}

The first method to remove baseline activity presented here is based on an additive ERSP model, which assumes that stimulus-induced spectral activity adds linearly to existing pre-stimulus spectral activity. This approach was first introduced by Tallon-Baudry et al. (

To compute this ERSP, the ERS trial average is normalized for each frequency band. In the baseline period – classically defined as the period preceding the stimulus – the average and standard deviation (SD) of power are first computed at each frequency. Then, the average baseline power is subtracted from all time windows at each frequency, and the resulting baseline-centered values are divided by the SD. For each time–frequency point of the time–frequency decomposition, the calculation of the ERSP can be formalized as follows:

where μ_{B}(

where _{B}(

The unit for ERSP_{z} values computed in Eq. _{z} and the mean baseline removal approach in terms of region of significance. It will therefore not be included in this report.

The gain model is detailed in Delorme and Makeig (

where μ_{B}( _{%} is percentage of baseline activity. The log-transformed measure is derived by taking the log value of ERSP_{%}:

The logarithmic scale of the last measure offers two advantages compared to the methods described previously. First, it has been shown by a large body of statistical signal processing literature that, for skewed signals such as EEG, the distribution of the logarithm of the signal is more normal than the distribution of the original signal. Therefore parametric inference testing is often more valid when applied to log-transformed power values – although in the case of the EEGLAB software, which we are using in this report, most statistics rely on surrogate methods which are not sensitive to the data probability distribution. The second advantage of logarithmic scales is that they allow visualizing a wider range of power variations, whereas for the absolute scales, power changes at low frequencies may mask power changes at high frequencies.

By definition, the unit of ERSP_{log} is Decibel (dB). Both measures ERSP_{%} and ERSP_{log} are commonly used in the literature (Fuentemilla et al.,

In the previous section we outlined different types of ERSP calculations applied to the ERS trial average. In this section, we are introducing methods to compute single-trial baseline correction. For each of the two ERSP models, namely the “additive model” and the “gain model,” the single-trial version of calculation is formalized below.

Instead of computing baseline normalization after trial averaging, baseline normalization is computed for each trial using the following equations:

where μ′_{B} (

σ′_{B} (

In the case of the gain model, we first divide each time–frequency point value by the average spectral power in the pre-stimulus baseline period at the same frequency. It is only after each trial has been baseline corrected that we compute the trial average. This is summarized in the following formal equations:

where μ′_{B} (

The log-transformed ERSP version is computed by taking the logarithm of ERSP_{TB − %}

Note that it would also be possible to compute the log of each trial and then average the results – which would be equivalent to computing the product of the time–frequency estimates across trials and then performing a log-transformation as:

However, calculating the product of single-trial spectral estimates might not be biological plausible. Moreover, it also leads to regularization issues. When the mean baseline power at a given frequency is too close to 0, the term defined in (11) would tend toward infinite. As a consequence, after log-transformation, the power of some trials could dominate the ERSP. This last approach has therefore not been considered in this report.

There is no need to perform classical baseline correction after single-trial baseline correction since, after single-trial pre-stimulus baseline correction, averaging values across trials preserves the baseline value. For instance, the baseline value for each trial is already centered at 0 for the ERSP_{TB − z} measure – after averaging trials the average baseline value remains 0. Similarly the average baseline value is 1 in ERSP_{TB − %}, and remains 1 after averaging trials.

This is important when computing statistics since the NULL hypothesis is based on trial-average baseline values: the general NULL hypothesis states that post-stimulus values do not differ from baseline values. Having a centered baseline is especially important for the “Bootstrap random polarity inversion” statistical method (see

In the results section, we show that single-trial baseline correction methods are biased. As a consequence we developed methods that normalize single-trials or centers them at 1 prior to applying standard baseline correction methods. We call these methods full-epoch length single-trial corrections, which, as we will see in the Section _{TB − z}, ERSP_{TB − %}, or ERSP_{TB − log} and consider the full-trial length for the “baseline” period instead of the pre-stimulus baseline. Note that the term “baseline” is not appropriate any longer in this case and is simply used to outline the calculation method. After computing ERSP trial averages, the average pre-stimulus values (actual pre-stimulus baseline) may differ from 0 (ERSP_{TB − z}, ERSP_{TB − log}) or from 1 (ERSP_{TB − %}). It is therefore important to recompute the classical trial average pre-stimulus baseline prior to computing statistics. This is formalized in the following paragraph: it consists in first performing full-epoch length single-trial correction, and then performing classical pre-stimulus baseline corrections on the resulting ERSP trial averages.

ERSP_{Full TB − z} is obtained by replacing raw spectral estimates |_{k}^{2} in Eqs _{Full TB − %} is obtained by replacing raw spectral estimates |_{k}^{2} in Eqs _{Full TB − log} is obtained by taking the log of ERSP_{Full TB − %} multiplied by 10.

We used two different statistical techniques to assess significance of ERSP results: one method is based on permutation of baseline period values at each frequency and another method is based on bootstrapping single-trial ERSP polarity at each time–frequency point. Note that after each procedure, the false discovery rate (FDR) procedure (Benjamini and Hochberg,

In this method, we considered the collection of single-trials and computed the surrogate distribution at each frequency by permuting baseline values across both time and trials. We therefore obtained one surrogate distribution per frequency and then tested if original ERSP values point lied in the 2.5 or 97.5% tail of the surrogate distribution at a given frequency. If it did, the specific time–frequency point was considered significant at

Single-trial power estimates need to be baseline corrected prior to applying this statistical procedure. However, for classical baseline correction methods (ERSP_{z}, ERSP_{%}, and ERSP_{log}), this method returns equivalent results if the statistical procedure is performed before or after baseline correction.

In this method, we randomly inverted the polarity of single-trial time–frequency power estimate after baseline correction. Randomly inverting the polarity means that on average only half of the values have their polarity inverted – although for each repetition, a different set of values is inverted. This statistical procedure is performed independently at each frequency point and is also applied to time–frequency point lying within the baseline period.

It is important to perform baseline correction on each trial prior to applying the statistical procedure since the polarity inversion of single-trial values depend on this baseline value.

For this statistical procedure, a surrogate distribution is computed at each time–frequency point – in contrast to each frequency for the statistical procedure described in Section

First, both classical and trial-based ERSP methods will be applied to artificial EEG data to demonstrate their fundamental properties. In a second step aiming to address the robustness of different ERSP methods, we introduced noisy data trials in a resting-state EEG dataset in which artificial spectral perturbations were added to background EEG activity. Finally we applied the methods to an actual EEG dataset taken from an animal/non-animal categorization task and analyzed the influence of noisy trials on ERSP results.

The first dataset used to study robustness of ERSP to noisy trials is an artificial dataset. It was created by mixing real EEG data recorded from a single subject and artificial spectral perturbations.

Electroencephalogram data was acquired using a Biosemi ActiveTwo system of 64 scalp electrodes placed according to the 10–20 system. The EEG signal was digitized at 2048 Hz with 24-bit A/D conversion, then down-sampled to 256 Hz. The data was then high-pass filtered at 0.5 Hz using a FIR filter and converted to averaged reference. Paroxysmal activity as well as periods containing electrical artifacts were removed by visual inspection of the raw continuous data.

Since the subject was not performing any task and no stimuli were presented, the continuous data should not contain any time-locked spectral activity. However, in order to simulate an evoked spectral response, mock events were first inserted in the raw continuous data every 3 s. Then, data epochs ranging from −1000 to 2000 ms relative to mock events were extracted for electrode Fp1, resulting in 58 non-overlapping 3000 ms segments. In each epoch, baseline was considered as the period starting 1000 ms before the mock event and ending at the mock event onset. Spectral perturbations were then modeled as an increase followed by a decrease in power in the 20 to 26 Hz frequency band. We artificially increased power for a finite time period from 300 ms to 799 ms after mock events, and reduced power from 1399 ms to 1599 ms.

To introduce spectral perturbations, first the time window to be perturbed was selected. Then a FFT was used on each EEG data trial for this time window. FFT coefficients corresponding to frequencies from 20 to 26 Hz were modified by adding or subtracting a fixed scalar (equal to 300). We finally computed an inverse FFT transform (using Matlab

The second set of EEG data came from an event-related EEG experimental paradigm (Delorme et al.,

To estimate the robustness of different ERSP models to noise, for both the artificial and the real EEG data described above, we added noise to a given percentage of data trials. To model noise in single-trials, an independent Gaussian noise with SD of five times the SD of the EEG data – computed over all time points and all data trials – was added to a random set of trials (in Figure

In order to evaluate the accuracy of the two different baseline correction methods, we first used the artificial EEG dataset containing the controlled spectral perturbation and computed confusion matrices for each ERSP method and for each percentage of noisy trials. We considered True Positives (TP, i.e., significant time–frequency estimates – or pixel in the ERSP image – included in the spectral perturbation area), False Positives (FP, i.e., significant time–frequency estimates outside of the spectral perturbation area), False Negatives (FN, i.e., non-significant time–frequency estimates inside the perturbation area) and True Negatives (TN, i.e., non-significant time–frequency estimates outside of the perturbation area). TP, FP, FN, and TN were expressed in percentage of the maximum number of time–frequency estimates in each category. Thus TP = 100% indicates that all time–frequency estimates in the perturbation area are significant, FN = 100 − TP indicates the percentage of time–frequency estimates within the perturbation which are not significant. Similarly, the maximum FP is reached when all the time–frequency estimates outside of the spectral perturbation area are significant. These measures allow evaluating the quality of each ERSP method through different metrics basically defined by signal detection theory and used in evaluation of classifiers or subject performances in categorization tasks (Green and Swets,

In addition, we computed the

Figure _{TB − log} (Figure _{TB − %} and ERSP_{TB − z} (not shown). Therefore performing single-trial baseline correction is sensitive to post-stimulus outliers and large positive post-baseline values are dominating the ERSP. One hypothesis is that pre-stimulus outliers affect the post-stimulus results as if the pre-stimulus data were stable, then the results would not be so sensitive to how the baseline subtraction is handled. However, the fact that this bias is observed with Gaussian noise disproves this hypothesis. The bias is a result of non-stationary of both the EEG signal and the computation method (Figure

_{TB − log} with single-trial baseline correction tends to produce large positively biased event-related post-stimulus spectral perturbations for both the real EEG data and the artificial Gaussian noise.

_{z} method _{TB − z} method _{Full TB − z} method

Figure

We then compared the performance of classical ERSP methods versus single-trial full-epoch length correction methods on artificial data using the baseline permutation statistical methods (Figure _{log} and ERSP_{Full TB − log}. We chose these two ERSP methods because they exhibited the best visual contrast (Figure _{Full TB − log}) and that FN increase at a slower rate when noisy trials are added. The rate of FP is globally higher for the single-trial-based correction method than for the classical one, except when the percentage of noisy trials is lower than 8%. The bootstrap random polarity inversion method for significant testing returned qualitatively similar results.

_{log} and ERSP_{Full TB − log}. The single-trial-based method (ERSP_{Full TB − log}) clearly outperforms the classical method (ERSP_{log}).

Figure _{log} and ERSP_{Full TB − log} methods.

Table _{z} and ERSP_{%}/ERSP_{log} methods for the two types of statistical inference methods when 8.6% of trials are noisy. Significance levels between classical correction and single-trial correction methods are computed using a bootstrap procedure as described in Section

_{z} and ERSP_{%}/ERSP_{log} methods for the two types of statistical methods when 8.6% of trials are noisy

Statistical method | |||||||
---|---|---|---|---|---|---|---|

Baseline permutation | Bootstrap random polarity inversion | ||||||

Classical correction | Single-trial correction | Classical correction | Single-trial correction | ||||

ERSP_{z} |
Sensitivity | 0.087 ± 0.11 | 0.77 ± 0.039 | 0.037 ± 0.033 | 0.82 ± 0.036 | ||

Specificity | 0.96 ± 0.02 | 0.94 ± 0.0087 | 0.91 ± 0.022 | 0.89 ± 0.0063 | |||

ERSP_{%}/ERSP_{log} |
Sensitivity | 0.083 ± 0.11 | 0.81 ± 0.029 | 0.038 ± 0.036 | 0.84 ± 0.036 | ||

Specificity | 0.96 ± 0.02 | 0.93 ± 0.012 | 0.91 ± 0.022 | 0.88 ± 0.0085 |

It may be argued that low sensitivity to noisy trials of the classical ERSP method depends on the level of the noise introduced. We thus used the same two ERSP methods on noisy trials with different amplitudes of noise. As described in the Section

_{Full TB − log}) clearly outperforms the classical method (ERSP_{log}) with a higher rate of True Positive significant values and a comparable rate of False Negative significant values.

Figure _{%} method. The region is slightly smaller for the ERSP methods based on single-trial correction than for the classical ERSP methods. We tested the hypothesis that single-trial methods were more sensitive to noise by replacing good trials by noisy ones as described in Section “Procedure to Model Noisy Trials and Assess Robustness of ERSP Model” and computed the ERSP_{log} and ERSP_{Full TB − log} for every number of noisy trials introduced in the signal. We observed that Region 2 was still significant and had the same extent for both classical and single-trial-based ERSP methods when 80% of noisy trials was introduced. Region 3 indicates a post-stimulus power decrease centered at about 13 Hz and spanning over the 10 to 15-Hz frequency band for the ERSP_{z} method. For the ERSP_{%} and the ERSP_{log} methods, a similar power decrease spans over the 6 to 15-Hz frequency band and is strongest at 6 Hz. This suggests that the variance across trials at 13 Hz is small compared to lower frequencies, which would explain why the power decrease at this frequency is larger in the ERSP_{z} method than in the ERSP_{%} and the ERSP_{log} methods. For all single-trial correction solutions, one additional significant region appears (region 4). This region corresponds to an early post-stimulus power increase in the 5 to 7-Hz frequency band. Note that the positive peak in the last panel of Figure

In Figure _{%}, ERSP_{z}, ERSP_{Full TB − %} and ERSP_{Full TB − z} methods were considered since the ERSP_{log} and ERSP_{Full TB − log} methods are mere log-transformation of the ERSP_{%} and ERSP_{Full TB − %} methods which do not modify the number of significant pixels. We also tried two methods for assessing significance: baseline permutation and bootstrap random polarity inversion (see

Table _{Full TB − z} method returned less significant pixels than the ERSP_{Full TB − %} method. For the bootstrap random polarity inversion statistical method, we also observed a significant effect of the baseline correction method [_{Full TB − z} method returned less significant pixels than the ERSP_{Full TB − %} method. In sum, ERSP using baseline normalization tends to return less significant pixels than ERSP using percentages of baseline. Classical baseline and single-trial correction methods also differed significantly although the method returning more significant pixel was contingent on the statistical method used to assess significance.

Baseline permutation | Bootstrap random polarity inversion | |||
---|---|---|---|---|

Classical correction | Single-trial correction | Classical correction | Single-trial correction | |

ERSP_{z} |
17.4 ± 7.8 | 14.4 ± 6.6 | 19.7 ± 5.7 | 20.2 ± 5.1 |

ERSP_{%}/ERSP_{log} |
17.6 ± 7.9 | 15.4 ± 6.7 | 19.7 ± 5.7 | 20.9 ± 5.0 |

In Figure _{z} and ERSP_{Full TB − z}) and percentage of baseline ERSP methods (respectively ERSP_{%} and ERSP_{Full TB − %}). It shows that if the percentage of noisy trials is greater than 2, the single-trial method gives more significant pixels than the classical method, although this difference decreases monotonically as the number of trials increases. Note that the percentage of significant pixels is not a true measure of sensitivity as the ones presented in Figure

_{z} and ERSP_{Full TB − z}). The second row represents data for time–frequency decompositions computed using percentage of baseline (ERSP_{%} and ERSP_{Full TB − %}). Classical ERSP baseline correction methods are represented in red and single-trial correction methods are represented in blue. Shaded areas represent SD which is estimated by adding noise to different random sets (

In order to further characterize the similarities of the ERSPs’ regions of significance, we computed the percentage of overlap between the significant regions of all pairs of ERSP methods for electrode Iz of 14 subjects (see

where _{s} is the number of pixels in the intersection of significant regions computed by ERSP methods _{s} is the number of pixels in the union of significant regions computed by ERSP methods

Figure _{%} and ERSP_{log} (respectively ERSP_{Full TB − %} and ERSP_{Full TB − log}), the differences observed between these two methods are due to random sampling in the bootstrap and permutation methods. Comparing Figure

At each time–frequency point, Figure _{%} and the ERSP_{Full TB − %} methods as well as the overlap between them. This innovative representation allows displaying the similarities (i.e., overlap, represented in yellow) and contrast between the two ERSP methods (in red and green). We observe that even if some regions exhibit a strong overlap especially at low frequencies (in bright yellow), some other areas are more specific to one or the other of the two ERSP methods (in bright red or bright green).

_{%} and ERSP_{Full TB − %} significant pixels across subjects and their overlap_{%} density of significant pixels is represented in green, ERSP_{Full TB − %} density in red, and the overlap between ERSP_{%} and ERSP_{Full TB − %} densities is shown in yellow. Density is coded by color saturation level, higher densities are shown with higher saturation level.

Figure _{%} (classical baseline correction) and ERSP_{Full TB − %} (single-trial correction) methods as well as the percentage of significant pixels for each frequency and time point. Results for the ERSP_{z} and the ERSP_{Full TB − z} methods are similar (not shown). Figure

_{%} and the ERSP_{Full TB − %} methods averaged over 14 subjects_{%} (classical baseline correction) and the ERSP_{Full TB − %} (single-trial correction) methods.

Figure _{z} and the ERSP_{Full TB − z} methods using the baseline permutation statistical method. This argues in favor of using these ERSP methods and the baseline permutation statistical test when it is important to minimize the number of significant values in the baseline period.

_{z}, _{Full TB − z}, _{%}, and ERSP_{Full TB − %} using the two statistical methods_{z} displayed in the upper row, and ERSP_{%} displayed in the lower row. Classical baseline correction methods are represented in red and single-trial correction methods are represented in blue. Shaded areas represent SE of the mean.

We have presented different ERSP methods, three based on classical baseline correction methods and three implementing single-trial correction methods. We showed the superiority of the single-trial correction methods on both artificial data and real data since these methods were less sensitive to noise compared to classical baseline correction methods. We also compared the number of significant time–frequency estimates and region of significance between all of these ERSP methods. For the data analyzed here, the overlap was strongest at low frequencies in the 200 to 1000 ms post-stimulus period. Moreover, the overlap between region of significance within classical baseline correction methods and within single-trial correction methods was always above 90%. This contrasts to 60–70% of overlap between the classical and the single-trial-based baseline correction methods and argues for a fundamental difference between these two types of approaches.

For single-trial correction methods, use of the entire time interval – including pre- and post-stimulus time intervals – may appear unconventional with respect to event-related approaches. However, processing that combines pre- and post-stimulus activity is a common procedure in EEG signal processing, as for example when performing filtering. Filtering is used in most EEG software. For example, performing high-pass FIR filtering at 0.5 Hz on continuous EEG data at 128 Hz usually requires a filter order or length of about 768. The convolution window thus comprises 6 s and might contain several stimuli: post-stimulus activity may affect pre-stimulus activity (and vice-versa), and we have observed this fact experimentally. Thus, our single-trial correction procedures combining pre- and post-stimulus activity fits well with the current EEG signal processing framework.

The main difference between the classical ERSP baseline correction methods and single-trial correction methods is that the single-trial correction approach is less sensitive to the presence of noisy trials. When adding noisy trials to the data, the number of significant pixels decreased exponentially for classical baseline correction methods. However, it decreased linearly for single-trial correction methods. This result is especially important because spectral transformations may amplify small trial noises. Even though EEG data might not appear noisy, power computed by taking the square of FFT amplitude tends to skew power distribution toward high positive values as shown in Figure

We have shown that the difference in terms of region of significance between classical baseline correction and single-trial correction methods is due to the high sensitivity of ERSP classical baseline correction to single-trial noise. This result strongly argues in favor of using single-trial correction methods when computing ERSP. Of all the methods presented in this report, we recommend using the ERSP_{Full TB − z} in conjunction with the baseline permutation statistical method for inference testing. ERSP_{Full TB − z} combined with this statistical method is robust to trial noise and has the lowest number of FP significant time–frequency points in the baseline period. All the methods presented in this article are implemented in the “newtimef” function of the EEGLAB software.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

This work was supported by a thesis fellowship from the French ministry of research and a grant from the FRM Foundation.