Denoising based on spatial filtering
Introduction
Magnetoencephalography (MEG) measures magnetic fields produced by brain activity using sensors placed outside the skull. The fields to be measured are extremely small, and they compete with strong fields from environmental noise sources (electric power lines, vehicles, etc.), sensor noise, and unwanted physiological sources (muscle activity, heart, eyeblinks, background brain activity, etc.).
Many methods have been proposed to combat noise (see Hämäläinen et al., 1993, Cutmore and James, 1999, Croft and Barry, 2000, Vrba, 2000, Volegov et al., 2004, Rong and Contreras-Vidal, 2006 for reviews). We recently proposed two new methods to target environmental noise (de Cheveigné and Simon, 2007) and sensor noise (de Cheveigné and Simon, 2008). In this paper, we present a third method that deals with biological noise that those previous methods did not address. The method involves spatial filtering, that is, replacing the recorded data by a set of linear combinations such that sources of interest are preserved and unwanted components are suppressed. Spatial filtering is involved in many MEG or EEG signal analysis techniques, such as beamforming or independent component analysis (ICA). We cast the problem in terms of denoising and offer a rational and flexible method for synthesizing the appropriate spatial filters.
Denoising involves a partition of the data into desirable components (signal) and undesirable components (noise). This is conceptually easier than the more ambitious task of analyzing the data into individual sources, such as performed, for example, by ICA. Separating the data into two parts requires milder assumptions than a complete analysis of all sources present. Validation is easier than for more general techniques, and the tools require less expertise and pose less risk of misuse by inexperienced practitioners. Denoised data have the same format as raw data, so that standard analysis tools may be applied to them, the only difference with raw data being better sensitivity and reduced risk that results are affected by noise.
In spatial filtering, each output channel is the weighted sum of input channels:where t is time, represents the K channels of raw data, the filtered data, and is the filtering matrix. Spatial filtering can be described in matrix format as:
Spatial filtering subsumes a wide range of operations. The simplest is to select an individual sensor channel (all except one), as in classic descriptions of EEG data using standardized electrode nomenclature, or a group of channels known to be sensitive to the phenomenon of interest (all except for k within the group) (e.g. Poeppel et al., 1996). More complex spatial filtering techniques are signal space projection (SSP) (Uusitalo and Ilmoniemi, 1997), signal space separation (SSS) (Taulu et al., 2005), spatiotemporal signal space separation (tSSS) (Taulu and Simola, 2006), beamforming Sekihara et al., 2001, Sekihara et al., 2006, principal component analysis (PCA) (e.g. Kayser and Tenke, 2003), independent component analysis (ICA) (e.g. Makeig et al., 1996, Vigário et al., 1998), the surface laplacian (e.g. Bradshaw and Wikswo, 2001), and other linear processing schemes Parra and Sajda, 2003, James and Gibson, 2003, Barbati et al., 2004, Cichocki, 2004, Tang et al., 2004, Delorme and Makeig, 2004, Nagarajan et al., 2006, Gruber et al., 2006. The spatial filter (or set of filters) enhances activity of interest and/or suppresses unwanted activity. Spatial filtering takes advantage of the spatial redundancy of high-density MEG or EEG systems, and is complementary with temporal filtering which takes advantage of the spectral structure of target and/or noise.
Our method belongs to the spatial filtering family. To synthesize the filter we rely on a recently-proposed method for semi-blind source separation known as denoising source separation (DSS) (Särelä and Valpola, 2005). In DSS, the K-channel sensor data are first spatially whitened by applying PCA and normalized to obtain a dataset with spherical symmetry, i.e. with no privileged direction of variance in K-dimensional space. The whitened data are then submitted to a bias function (which Särelä and Valpola, 2005 call “denoising function”) followed by a second PCA that determines orientations that maximize the bias function. This second PCA produces a transformation matrix that is finally applied to the whitened (but not biased) data. The result of DSS analysis is a set of components ordered in terms of decreasing susceptibility to bias. Throughout this paper, the bias function is chosen to be the proportion of epoch-averaged (evoked) activity. However, other bias functions may be used and the DSS method is of wider applicability than described here.
Our focus here is denoising rather than data analysis. The method that we propose is intended to complement, by use as a denoising preprocessor, other techniques for brain source analysis and source modeling.
Section snippets
Signal model
Sensor signals include interesting “target” activity and uninteresting “noise” activity:
The first term results from the superposition of sources of interest within the brain:where is a mixing matrix. The second term results from the superposition of various noise sources in the environment, sensors, and subject’s body:where is a second mixing matrix. Our aim is to attenuate
Results
Fig. 1(a) shows the percentage of power carried by each DSS component before (black) and after (red) averaging. In both cases, the values are normalized to add up to 100%. For the raw signal (black) all components have roughly the same order of magnitude, but for the evoked signal (red) the low-order components carry most of the power. Fig. 1(b) shows the percentage of power that would be retained if the component series were truncated beyond a given component before (red) and after (black)
Discussion
The method reduces noise effectively in stimulus-evoked response paradigms.
Acknowledgments
Thanks to Israel Nelken, Jaakko Särelä and Harri Valpola and Jonathan Le Roux for insight. Harri Valpola and two anonymous reviewers offered useful comments on an earlier manuscript. This work was partly supported by a collaboration grant with NTT Communications Research Laboratories. J.Z.S. was supported by NIH-NIBIB grant 1-R01-EB004750D01 (as part of the NSF/NIH Collaborative Research in Computational Neuroscience Program).
References (36)
- et al.
Optimization of an independent component analysis approach for artifact identification and removal in magnetoencephalographic signals
Clin Neurophysiol
(2004) - et al.
Removal of ocular artifact from the EEG: a review
Neurophysiol Clin
(2000) - et al.
Identifying and reducing noise in psychophysiological recordings
Int J Psychophysiol
(1999) - et al.
Denoising based on time-shift PCA
J Neurosci Methods
(2007) - et al.
Sensor Noise Suppression
J Neurosci Methods
(2008) - et al.
EEGLAB: an open toolbox for analysis of single-trial EEG dynamics including independent component analysis
J Neurosci Methods
(2004) - et al.
Denoising using local projective subspace methods
Neurocomputing
(2006) - et al.
Optimizing PCA methodology for ERP component identification and measurement: theoretical rationale and empirical evaluation
Clin Neurophysiol
(2003) - et al.
A graphical model for estimating stimulus-evoked. Brain responses in noisy MEG data with large background brain activity
Neuroimage
(2006) - et al.
Task-induced asymmetry of the auditory evoked M100 neuromagnetic field elicited by speech sounds
Cogn Brain Res
(1996)
Magnetoencephalographic artifact identificatiion and removal based on independent component analysis and categorization approaches
J Neurosci Methods
Detecting and correcting for head movements in neuromagnetic measurements
Neuroimage
Sampling theory for neuromagnetic detector arrays
IEEE Trans Biomed Eng
Electromagnetic brain mapping
IEEE Sig Proc Mag
Spatial filter approach for evaluation of the surface Laplacian of the electroencephalogram and magnetoencephalogram
Ann Biomed Eng
Blind signal processing methods for analyzing multichannel brain signals
Int J Bioelectromagnet
Introduction to the bootstrap. Monographs on statistics and applied probability
Transformation for ordering multispectral data in terms of image quality with implications for noise removal
IEEE Trans Geosci Remote Sens
Cited by (158)
Cross-modal implicit learning of random time patterns
2023, Hearing ResearchThe power of rhythms: how steady-state evoked responses reveal early neurocognitive development
2022, NeuroImageCitation Excerpt :The cluster of electrodes can be defined based on the existing literature (Boremanse et al., 2013; Peykarjou et al., 2017), or based on the evoked response of the targeted sensory modality (Doelling et al., 2019). Another possibility for reducing the dimensionality of the data entails the implementation of spatial filters, whereby a single ideal electrode is constructed as a weighted sum of all electrodes to optimally separate the signal from the noise (M. X. Cohen and Gulbinaite, 2017; de Cheveigné and Parra, 2014; de Cheveigné and Simon, 2008). Alternatively, clustering and permutation algorithms can be used to control for multiple comparisons across electrodes, and identify the spatial distribution of the experimental effects (Kabdebon et al., 2015).
Recording EEG in cochlear implant users: Guidelines for experimental design and data analysis for optimizing signal quality and minimizing artifacts
2022, Journal of Neuroscience MethodsAutomated Pipeline for Infants Continuous EEG (APICE): A flexible pipeline for developmental cognitive studies
2022, Developmental Cognitive Neuroscience