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MEG SIGNAL DENOISING BASED ON TIME-SHIFT PCAAlain de Cheveign´e∗, Jonathan Le Roux∗†and Jonathan Z. Simon‡∗CNRS, Universit´e Paris 5 and Ecole Normale Sup´erieure, [email protected]†Information Science and Technology, The University of Tokyo, [email protected]‡Electrical & Computer Engineering/Biology, University of Maryland, [email protected] present a method for removing environmental noisefrom physiological recordings such as Magnetoencephalogra-phy (MEG) for which noise-sensitive reference channels areavailable. Sensor signals are projected on a subspace spannedby the reference channels augmented by time-shifted and/ornonlinearly transformed versions of the same, and the pro-jections are removed to obtain “clean” sensor signals. Themethod compensates for scalar, convolutional or non-linearmismatches between sensor and reference channels by syn-thesizing, for each reference/sensor pair, a filter that is opti-mal in a least-squares sense for removal of the artifact. Themethod was tested with synthetic and real MEG data, typ-ically removing up to 98% of noise variance. It offers analternative to bulky and costly magnetic shielding (multiplelayers of aluminium and mu-metal) for present scientific andmedical applications and future developments such as brain-machine interfaces (BMI).Index Terms— Magnetoencephalography, Bioelectric po-tentials, Biomedical imaging, Interference suppression1. INTRODUCTIONIn magnetoencephalography (MEG), superconducting quan-tum interference device (SQUID) sensors placed outside theskull measure magnetic fields produced by brain activity [2].Brain fields are extremely small, several orders of magnitudebelow environmental noise produced by sources such as elec-tric power lines and mechanical elevators. Despite measuressuch as magnetic and electromagnetic shielding (multiple lay-ers of aluminium and mu-metal), active noise field cancella-tion, and the use of gradiometers which are more sensitive tothe inhomogenous field produced by proximal sources thanthe homogenous field of more distant noise sources [3, 4],recorded signals may be dominated by noise. Shielding, inparticular, is expensive and bulky, and this is an obstacle tothe deployment of MEG for scientific and medical applica-tions, or the development of practical brain-machine inter-faces (BMI).Several noise-reduction techniques use reference sensorsthat respond primarily to noise sources to estimate their con-tribution to brain sensors, and remove that contribution. Ourmethod follows the same spirit but with an original twist:sensor channels are augmented by various transforms (delaysand non-linearity) that allow it to handle convolutive and/ornonlinear mismatches between sensors. The examples thatwe give to illustrate the method are from an MEG machineequipped with three magnetometer sensors sensitive to thehomogenous field of distant sources. The method is howeverof use for other MEG configurations, and for other sensitivephysiological recording techniques such as EEG, local fieldpotentials, single-units, etc. for which environmental noise isa problem.The method is a generalization of Principal ComponentAnalysis (PCA). PCA is a linear transformation that “rotates”a set of data of dimension K, expressing each as a sum of Kone-dimensional components (“principal components”) thatare (a) mutually orthogonal to each other, and (b) orderedin terms of variance from large to small. The total variance(or power) is conserved. Components are ordered with de-creasing variance, and therefore as much variance as possibleis “packed” into the first components. If the data set is oflower dimensionality than the space, i.e. it fits within a “hy-perplane”, later components may be discarded without loss.PCA is thus useful for dimensionality reduction. PCA is oftenused as an ingredient in denoising algorithms [5, 6, 7, 8, 9].Here we use PCA in combination with subspace projectionto synthesize, for each reference/target channel pair, a filterthat maximizes the proportion of noise that can be suppressed.The goal is to provide a simple and effective means for reduc-ing the impact of environmental noise on data recorded fromMEG or other noise-sensitive techniques.2. SIGNAL MODELTwo sets of signals are observed: data sensor signals s(t)=[s1(t), ··· ,sK(t)]and noise reference signals r(t)=[r1(t),··· ,rJ(t)]. The data sensor signals reflect a combination ofbrain activity and environmental noise:s(t)=sB(t)+sE(t) (1)whereas the J reference sensors reflect only noise. We ap-proximate this situation using three signal models of increas-I  3171424407281/07/$20.00 ©2007 IEEE ICASSP 2007ing complexity. In a first model, the multiple sources of envi-ronmental noise contribute to both sets of sensors via scalarmixing matrices:sE(t)=An(t) (2)r(t)=Bn(t)where A =[akl] and B =[bjl] are the mixing matrices andn(t)=[n1(t), ··· ,nL(t)]represents the L noise sources.The brain term, sB(t), also depends on multiple sources withinthe brain but the details of this dependency do not interest ushere. Scalar mixing is not an unreasonable assumption, giventhat the propagation of magnetic fields is practically instan-taneous. A second model assumes a similar dependency ofsensor signals on noise sources, but via convolutional mixingmatrices. Assuming convolution instead of multiplication inEq. 2, each element aklor bjlof the mixing matrices A or Bnow represents an impulse response, e.g.:rj(t)=(bjl∗ nl)(t) (3)This second model can handle the effects of hardware filterswithin sensor channels (e.g. high-pass, notch, or antialias-ing), as well as any spectral distortion or time shift that mightoccur within the sensor itself. The third model extends thesecond by allowing noise components to undergo non-lineartransformations before and/or after mixing:sE(t)=A[n(t)] (4)r(t)=B[n(t)]where A and B are non-linear functions with memory (fil-ters). This third model allows for non-linearities in the mixingmechanism, and/or in the sensors.3. ALGORITHMS AND IMPLEMENTATIONOur goal is to find a function F to apply to the reference sig-nals so that F [r(t)] is as close as possible to sE(t) so thatby subtraction we obtain the best possible measurement ofsB(t):sB(t)=s(t) − F [r(t)]. (5)For the first model the solution is to simply project each targetsignal on the subspace spanned by the reference sensors. Thisinvolves finding a matrix C

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