Denoising based on spatial filtering

https://doi.org/10.1016/j.jneumeth.2008.03.015Get rights and content

Abstract

We present a method for removing unwanted components of biological origin from neurophysiological recordings such as magnetoencephalography (MEG), electroencephalography (EEG), or multichannel electrophysiological or optical recordings. A spatial filter is designed to partition recorded activity into stimulus-related and stimulus-unrelated components, based on a criterion of stimulus-evoked reproducibility. Components that are not reproducible are projected out to obtain clean data. In experiments that measure stimulus-evoked activity, typically about 80% of noise power is removed with minimal distortion of the evoked response. Signal-to-noise ratios of better than 0 dB (50% reproducible power) may be obtained for the single most reproducible spatial component. The spatial filters are synthesized using a blind source separation method known as denoising source separation (DSS) that allows the measure of interest (here proportion of evoked power) to guide the source separation. That method is of greater general use, allowing data denoising beyond the classical stimulus-evoked response paradigm.

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 s˜k(t) is the weighted sum of input channels:s˜k(t)=k=1Kakksk(t)where t is time, S(t)=[s1(t),,sK(t)]T represents the K channels of raw data, S˜(t)=[s˜1(t),,s˜K(t)]T the filtered data, and A=[akk] is the filtering matrix. Spatial filtering can be described in matrix format as:S˜(t)=AS(t).

Spatial filtering subsumes a wide range of operations. The simplest is to select an individual sensor channel (all akk=0 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 akk=0 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 S(t)=[s1(t),,sK(t)]T include interesting “target” activity and uninteresting “noise” activity:S(t)=SB(t)+SN(t).

The first term results from the superposition of sources of interest B(t)=[b1(t),,bJ(t)]T within the brain:SB(t)=ABB(t)where AB is a mixing matrix. The second term results from the superposition of various noise sources N(t)=[n1(t),,nJ(t)]T in the environment, sensors, and subject’s body:SN(t)=ANN(t)where AN is a second mixing matrix. Our aim is to attenuate SN(t)

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).

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