Automatic and robust noise suppression in EEG and MEG: The SOUND algorithm

Highlights

• We present the SOUND algorithm that is based on the optimal Wiener-filtering.

• SOUND automatically identifies and suppresses noise in multichannel MEG/EEG data.

• SOUND surpasses the common channel-rejection and interpolation scheme.

• Running SOUND takes significantly less time compared to visual data inspection.

• The MATLAB implementation of SOUND is provided in a freely downloadable demo package.

Abstract

Electroencephalography (EEG) and magnetoencephalography (MEG) often suffer from noise- and artifact-contaminated channels and trials. Conventionally, EEG and MEG data are inspected visually and cleaned accordingly, e.g., by identifying and rejecting the so-called ”bad” channels. This approach has several shortcomings: data inspection is laborious, the rejection criteria are subjective, and the process does not fully utilize all the information in the collected data.

Here, we present noise-cleaning methods based on modeling the multi-sensor and multi-trial data. These approaches offer objective, automatic, and robust removal of noise and disturbances by taking into account the sensor- or trial-specific signal-to-noise ratios.

We introduce a method called the source-estimate-utilizing noise-discarding algorithm (the SOUND algorithm). SOUND employs anatomical information of the head to cross-validate the data between the sensors. As a result, we are able to identify and suppress noise and artifacts in EEG and MEG. Furthermore, we discuss the theoretical background of SOUND and show that it is a special case of the well-known Wiener estimators. We explain how a completely data-driven Wiener estimator (DDWiener) can be used when no anatomical information is available. DDWiener is easily applicable to any linear multivariate problem; as a demonstrative example, we show how DDWiener can be utilized when estimating event-related EEG/MEG responses.

We validated the performance of SOUND with simulations and by applying SOUND to multiple EEG and MEG datasets. SOUND considerably improved the data quality, exceeding the performance of the widely used channel-rejection and interpolation scheme. SOUND also helped in localizing the underlying neural activity by preventing noise from contaminating the source estimates. SOUND can be used to detect and reject noise in functional brain data, enabling improved identification of active brain areas.

Introduction

Electroencephalography (EEG) and magnetoencephalography (MEG) are non-invasive functional imaging methods that are able to record post-synaptic neural activity with excellent temporal resolution. Because MEG and EEG sensors are very sensitive, they are highly susceptible to noise contamination (Ferree et al., 2001, Vrba and Robinson, 2001), which may lead to erroneous interpretations of the cortical activity. We present an effective way to clean noisy EEG/MEG signals by optimally utilizing the multi-sensor data with the help of Wiener estimation. The suggested technique makes use of the bioelectromagnetic model of the head to distinguish noise from neural signals.

Common approaches to deal with noisy data are frequency-domain filtering and the visual identification and rejection of poor-quality sensors or data segments (e.g., Styliadis et al., 2014, Van der Meer et al., 2013, Tewarie et al., 2014, Dominguez et al., 2014). However, the frequency range of the noise may not have well-specified limits, or the noise spectra and the neural spectra of interest may overlap (Herrmann and Demiralp, 2005, Jensen and Colgin, 2007, Monto et al., 2008). Second, visual inspection of the data is laborious, and making rejection decisions is highly subjective. Finally, rejecting sensors always reduces the data dimensionality (amount of information), which cannot be regained even if interpolation is used to reconstruct the data.

We present an objective and robust methodology to quantify noise levels in different parts of the data and to correct the measured signals in a way that optimally utilizes the gathered multidimensional information. We call this approach the source-estimate-utilizing noise-discarding algorithm (the SOUND algorithm, hereafter referred to as SOUND). SOUND detects noise automatically by assessing, with the help of a forward model, how well the signal in each channel can be predicted from the rest of the signals. Each sensor is then corrected based on the signal-to-noise-ratio (SNR) values of all the recording sensors.

We show that SOUND is a special case of a more general class of Wiener estimators, which minimize the mean-squared error in estimating the noiseless signal. In addition to SOUND, an alternative Wiener-estimation approach, which can be computed based only on the recorded data samples, is discussed. In this paper, we refer to this general technique as data-driven Wiener (DDWiener). By applying the DDWiener approach to event-related responses, we illustrate how the noise in individual trials can be automatically detected and taken into account so that the SNR of the estimated evoked response is maximized. The presented data-correction methods work automatically and without completely rejecting any dimension in the data.

For MEG analysis, powerful noise-cleaning techniques that utilize physical principles to separate noise from the multi-sensor signals, e.g., signal-space separation (SSS) (Taulu et al., 2004, Taulu and Kajola, 2005) and the generalized side lobe canceller (Mosher et al., 2009), have been taken into use. Another common approach in MEG is to measure the environmental noise signals from an empty MEG room prior to subject entering the recording space. The noisy signal-space directions can then be rejected from the actual data, e.g., by using signal-space projection (SSP) (Uusitalo and Ilmoniemi, 1997).

SSP can be used to clean certain EEG artifacts (Mäki and Ilmoniemi, 2011, Mutanen et al., 2016), but it is often difficult to determine the poor-quality signal directions as the empty-room measurement is not possible. In practice, the most common approach to tackle the sensor-specific noise is to identify and reject the noisy channels and to interpolate the data in the rejected channels using, e.g., the spherical-spline basis functions (Perrin et al., 1989) or source modeling (Mutanen et al., 2016, Nieminen et al., 2016). One may also build a surrogate model that describes the brain-derived and the artifactual EEG simultaneously to clean the data (Litvak et al., 2007, Berg and Scherg, 1994); for this purpose, the artifact topographies need to be defined, e.g., with the help of principal component analysis.

If the data contain artifacts that can be characterized by few topographies and the corresponding time-domain samples arise from non-Gaussian distributions, independent components analysis (ICA) may also be useful in cleaning the data (Vigário, 1997, Korhonen et al., 2011). Artifactual ICA components are often identified and rejected manually but also some automatic methods have been suggested, e.g., FASTER (Nolan et al., 2010), which uses a set of predefined artifactual features to categorize the obtained ICA components into brain and noise components. However, it is not always true that the noise sources follow the assumptions of ICA.

All the above-mentioned EEG-correction techniques require that the contaminated data are confined to only a few channels or signal-space directions, which are identifiable based on the amplitudes or the distributions of the data samples. It should be noted that these techniques decrease the dimensionality of the data and they may require a notable amount of heuristic knowledge.

Possibly, the algorithm closest to SOUND is Sensor Noise Suppression (SNS) (De Cheveigné and Simon, 2008), which corresponds to DDWiener in the sensor space. As SOUND, SNS detects noise in MEG and EEG channels by comparing the signal in each sensor to the rest of the sensor traces. In SNS, each sensor signal is replaced by that part of the original signal belonging to the signal subspace spanned by the other sensor signals. SNS works well with noise that is completely uncorrelated across different sensors as well as uncorrelated with the brain signal, but it is very sensitive to violations of these assumptions.

As EEG noise cannot be estimated from an empty-room measurement, we here concentrate on studying the performance of SOUND and general Wiener estimation with EEG. We illustrate through sample datasets how SOUND improves EEG signal quality. With simulations, we demonstrate that SOUND improves SNR, is robust against modeling errors, and can improve source localization. We compare the performance of SOUND to the most commonly applied method, the channel rejection and interpolation, as well as to SNS. As a proof of concept, we show that SOUND can also be used to clean evoked MEG data.