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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 1, JANUARY 2004

Performance of an MEG Adaptive-Beamformer
Source Reconstruction Technique in the Presence of
Additive Low-Rank Interference
Kensuke Sekihara*, Srikantan S. Nagarajan, David Poeppel, and Alec Marantz

Abstract—The influence of external interference on neuromagnetic source reconstruction by adaptive beamformer techniques
was investigated. In our analysis, we assume that the interference
has the following two properties: First, it is additive and uncorrelated with brain activity. Second, its temporal behavior canbe characterized by a few distinct activities, and as a result, thespatio-temporal matrix of the interference has a few distinctly
large singular values. Namely, the interference can be modeled
as a low-rank signal. Under these assumptions, our analysis
shows that the adaptive beamformer techniques are insensitive tointerference when its spatial singular vectors are so different froma lead field vector of a brain source that the generalized cosine
between these two vectors is much smaller than unity. Four typesof numerical examples verifying this conclusion are presented.
Index Terms—Adaptive beamformer, biomagnetism, functional
neuroimaging, magnetoencephalography, MEG inverse problems,
neuromagnetic signal processing.

I. INTRODUCTIONNEUROMAGNETIC measurements are often contaminated by various types of overlapping externalinterference even when the measurements are performed in amagnetically shielded room. Typical examples of such interference include magnetic noise from power lines or electric
appliances such as elevators, automobiles or the subway. Small
vibrations in neuromagnetometer hardware can cause large
noises. Cardiac motions, muscle movements, or eye-blinks canalso interfere with neuromagnetic measurements.
Recently developed external noise cancellation techniques[1] reduce such interference to some extent. However, when theinterference is very large, a significant amount may still remain
Manuscript received January 20, 2003; revised May 11, 2003. The work of
K. Sekihara was supported in part by Grants-in-Aid from the Kayamori Foundation of Informational Science Advancement, in part by Grants-in-Aid from
Magnetic Health Science Foundation, and in part by the Ministry of Education,
Science, Culture and Sports in Japan under Grant-in-Aid C13680948. The workof S. S. Nagarajan was supported in part by the Whitaker Foundation and inpart by the National Institute of Health (NIH) under Grant P41RR12553-03 andGrant R01-DC004855-01A1. The work of D. Poeppel was supported in part by
the National Institute of Health (NIH) under Grant NIH-R01-DC5660. Asterisk
indicates corresponding author.
*K. Sekihara is with the Department of Electronic Systems and Engineering,Tokyo Metropolitan Institute of Technology, Asahigaoka 6-6, Hino, Tokyo 1910065, Japan (e-mail: ksekiha@cc.tmit.ac.jp).
S. S. Nagarajan is with the Department of Radiology, University of California,
San Francisco, San Francisco, CA 94143 USA.
D. Poeppel is with the Department of Linguistics and Biology, University of
Maryland, College Park, MD 20742 USA.
A. Marantz is with the Department of Linguistics and Philosophy, Massachusetts Institute of Technology, Cambridge, MA 02139 USA.
Digital Object Identifier 10.1109/TBME.2003.820329

in the recordings. Also, external noise cancellation cannot workwhen the interference is sensor-channel specific, i.e., when
it exists only in certain sensor recordings. This can happen,
for example, when some sensors are particularly sensitive toa certain type of vibration but other sensors are not. When
we estimate source distributions from magnetoencephalogram(MEG) measurements, the above-mentioned interferences
generally cause severe errors in the final estimations.
A class of source estimation methods called adaptive beamformer techniques have attracted great interest. Adaptive-beamformer techniques were originally developed in the fields ofarray signal processing [2], and they have been successfully applied to neuromagnetic source reconstruction problems [3]–[7].
In this paper, we analyze the influence of external interference
on the adaptive beamformer reconstruction results. Our analysis
assumes the following properties: First, the interferences are additive and uncorrelated with brain signals. Second, the temporal
behavior of the interference can be characterized by only a few
distinct activities and, as a result, the covariance matrix of theinterference has only a few distinctly large eigenvalues. Namely,
the interference can be modeled as a low-rank signal.
Our analysis shows that adaptive beamformer techniques areinsensitive to such interference when the eigenvectors of the covariance matrix are very different from the source lead field vectors. Since many types of interference with artificial (nonbiological) origins should have eigenvectors very different from thelead field of a brain source, we can conclude that the adaptive
beamformer techniques are generally robust to the overlaps ofsuch interference. In this paper, Section II briefly reviews adaptive-beamformer techniques for neuromagnetic reconstruction.
Section III presents our theoretical analysis. Section IV presents
the results of several numerical experiments that validate the arguments in Section III. Throughout this paper, plain italics indicate scalars, lower-case boldface italics indicate vectors, andupper-case boldface italics indicate matrices. The eigenvalues
are numbered in decreasing order.

II. ADAPTIVE-BEAMFORMER TECHNIQUES FOR
NEUROMAGNETIC RECONSTRUCTION
A. Definitionsth
We define the magnetic field measured by theas, and a column vector
detector coil at time
as a set of measured datais the total number of detector coils and superscriptwhere0018-9294/04$20.00 © 2004 IEEE

SEKIHARA et al.: PERFORMANCE OF AN MEG ADAPTIVE-BEAMFORMER SOURCE RECONSTRUCTION TECHNIQUE

indicates the matrix transpose. The spatial location is rep.
resented by a three-dimensional (3-D) vector :The covariance matrix of the measurement is denoted as , i.e.,. A total of
discrete sources are assumed
to generate the neuromagnetic field, and the locations of these. The moment magnitude
sources are denoted as. The orientation of the thof the th source is denoted assource is defined as a 3-D vector
whose
component (where equals , , or ) is equal to the cosine of
the angle between the direction of the source moment and the
direction. We define
as the output of the th sensor. The
output is induced by the unit-magnitude source located at andis defined
directed in the direction. The column vector. The lead field matrix,
aswhich represents the sensitivity of the whole sensor array at ,. The lead-field vector
is defined asin the source-moment direction is defined as
where.
B. Adaptive-Beamformer Source Reconstruction
To solve neuromagnetic source reconstruction problems,
we focus on the class of techniques referred to as the adaptive
beamformer, which was originally developed in the field ofarray signal processing [2], [8]. One well-known adaptive
beamformer is the minimum-variance beamformer [9], andtwo kinds of extensions have been proposed to incorporate the3-D vector nature of sources in neuromagnetic reconstruction.
One kind, called the scalar beamformer, uses the following
formulation:
(1)
where
is the estimated source-moment time course
obtained as the beamformer output. The weightis deunder the constraint thatrived by minimizing. The explicit form of the scalar-type weightis known to be [3](2)Note that the weight in (2) depends not only on the spatial location but also on the orientation , and therefore, informa.
tion regarding the source orientation is needed to calculate
Using this weight, the time-averaged source power is obtained
from [3](3)The other kind of extension, called the vector-type beamformer, enables the simultaneous estimation of the source orientation and source magnitude. It uses a set of three weight vectors,,, and, each of which estimates the ,, and components of the source moment. A set of weights
for a vector-extended minimum-variance beamformer is givenby [10], [11](4)91

The , , and components of the source moment are estimatedfrom(5)
is the estimated source moment in the direction
where, , or ). The magnitude of the source moment is esti(
mated from(6)
, and is the estiwheremated source orientation obtained using (5). It can be shown thatis mathematically equivalent to the scalar
the weight
beamformer weight in (2) with giving the maximum beamformer outputs [12]. Therefore, in our following analysis, we
use the scalar beamformer formulation for simplicity, but theobresults of the analysis are also valid for the weighttained from the vector beamformer formulation.
III. BEAMFORMER PERFORMANCE WHEN ADDITIVE
LOW-RANK INTERFERENCE EXISTSth sensor
We denote the interference carried by theas. The column vector
channel at time
represents the interference contained in
the measurements of the whole sensor array. We assume thatis additive, so the measured data
is expressed as
(7)
where
(8)
and
is the sensor noise that can be modeled using awhite Gaussian random process uncorrelated between sensor,
channels. The power of the sensor noise is denoted as
and it is assumed to be equal for all channels. We define theas , suchspatio-temporal matrix of the measurement. Here,are the timethat
points where the measurements are taken. The spatio-temporal, is defined as:
matrix of the source signal plus noise,, and the spatio-temporal matrix:. Then,of the interference as
relationshipholds.
, as
We next define the covariance matrix obtained from, i.e.,. We also define the covariance ma. Assumingtrix of the interference as , i.e.,
is uncorrelated with, we derive thethat interference
relationship(9)and from (1), the output of the beamformer is given by
(10)
where
. Here, we omit the explicit notations ofand from the lead field vector for simplicity.

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The key assumption forin our analysis is thatis alow-rank matrix and has only a few distinctly large eigenvalues.
can be expressed asThat is,(11)
andare the th eigenvalue ofand its correwhereis the number of nonzero eigensponding eigenvector. Here,. In this case, using thevalues, and we assume thatsingular value decomposition, the spatio-temporal matrix
isexpressed asthat the interference affects the output through its spatial singular vector by modifying the lead field vector into according to (15).
When the brain sources are well separated from each other,neglecting the sensor noise, the beamformer output at the thwithsource location is derived by replacingin (17). Denoting
as , the time course output is expressed as(12)
is the th temporal singular vector of. We firstwhere
is a rank-one matrix. In suchanalyze the simplest case whereiscases, omitting the subscript for eigenvalue numbering,
expressed as. Then, we derive(13)
where we use the relationship. Because(the proof is presented in Appendix) and thepower of the interference is equal to , this relationship holds
under the assumption that the power of the interference is muchlarger than the power of the sensor noise.
into (10), we obtain
Substituting (13) and(18)
and its power output is given by(19)
In the above equations, the generalized cosine with the metricbetween two column vectors
andis defined as(20)
Because the definition of the generalized cosine is very similar
to the correlation coefficient, the generalized cosine can quantify the similarity or the difference of the two vectors. Thus,
when any lead field vector in the source space is very different
from the spatial eigenvector of the interference , the relationships
and
hold.
When these relationships hold, (18) and (19) can be changed
to
(21)
and

(14)

(22)

where
(15)
Using (13), the value ofis found to be(16)

These equations clearly indicate that influence of the interference is negligible in such cases.
is a rank-one matrix. The
So far, our analysis assumes thatis a rank-two maanalysis can be extended to the case where
trix. In this case,andare expressed asand. Substituting theseequations into (10) and assuming the relationships

Therefore, substituting (16) into (14), we finally derive
and

(23)

(17)
after lengthy calculations, we finally get
The above equations indicate that the temporal behavior of theinterference represented by the temporal singular vector does
not affect the beamformer output. These equations also indicate(24)

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93

where
(25)
We can then derive (26) and (27) as shown at the bottom of page.
These equations show that the second eigenvector affects the
beamformer outputs in an additive manner and, therefore, the influence from this eigenvector is negligible if. The analysis can be further extended to the general case whereis equal to, and it can be shown that eachthe rank ofeigenvector influences the beamformer outputs in exactly thesame additive manner.
IV. NUMERICAL EXPERIMENTS
A series of numerical experiments were conducted to checkthe validity of the analysis in Section III. A sensor alignmentof the 148-sensor array from Magnes 2500 (4D Neuroimaging
Inc., San Diego, CA) neuromagnetometer was used. The coordinate origin was set at the center of the sensor coil located at thecenter of the coil array. The direction was defined as that fromposterior to anterior, the direction was defined as that from theright to the left hemisphere, and direction was defined as thatperpendicular to the surface of the coil at the origin. Three point.
sources were assumed to exist on a plane defined as(The values of the spatial coordinates ( , , ) are expressed incentimeters.) The source-sensor configuration and the coordinate system are illustrated in Fig. 1.
The simulated magnetic recordings were calculated in the following manner. We denote the locations and orientations of theand(, 2, 3), which are listed inthree sources as,
Table I. The lead field vectors of the three sources,, 2, 3) by using the spherically homogewere calculated (neous conductor model [13] with its center set at (1, 0, 11). We
then calculated the simulated magnetic-field recordings such
, where the time courses
that
,
, and
were calculated by using

forFig. 1. The coordinate system and source-sensor configuration used in the
numerical experiments. The coordinate origin was set at the center of the sensor
coil located at the center of the array. The plane at x = 1:0 cm is shown.
The large circle shows the cross section of the sphere used for the forward
calculation, and the square shows the reconstruction region used for the resultsin Figs. 2(c) and 6.

TABLE I
SOURCE PARAMETER VALUES USED FOR THE
NUMERICAL EXPERIMENTS IN SECTION IV

TABLE IIVALUES OF THE PARAMETERS USED FOR CALCULATING s (t),s (t), AND s (t)

and
(28)

In the above equations, , , , andare the numericalparameters controlling the shapes of the time courses, and theirvalues are listed in Table II. The three time courses are shownin Fig. 2(a). The magnetic-field recordings were calculated

(26)
and
(27)

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Fig. 2. (a) Time courses s (t), s (t), and s (t) (from top to bottom) used for the numerical experiments. (b) The simulated magnetic-field recordings, whichwere calculated at 2-ms intervals from zero to 800 ms. White Gaussian noise was added in order for the SNR to equal eight. (c) The average power reconstruction
hs(r; t) i obtained using the simulated magnetic field recordings in (b).

at 2-ms intervals from zero to 800 ms. The amplitude of
was set so that the resulting
the white Gaussian noise
signal-to-noise ratio (SNR) was eight where the SNR is definedandindicates the time averageasover 800 ms. The simulated magnetic-field recordings areshown in Fig. 2(b). The source reconstruction was performed
wasusing (3). In the reconstruction, the covariance matrix.
calculated using
The results of source-power reconstruction obtained with thisare shown in Fig. 2(c), which shows the reconstruction
when no interference exists.
In our numerical experiments, four types of interference
were simulated. The first was the periodic interference where, was calthe interference for the th sensor recording,for 60 sensors overculated using
for other sensors. The
the right hemisphere andfrequency of this periodic interference
was set at 13.7 Hz,
which is very close to the 10 Hz-frequency of the third source.
was then added to the signal magnetic
The interference
to generate simulated magnetic-field recordings:
field. The resultant simulated recordings areshown in Fig. 3(a).
The second type of interference was the same periodic interference except that the phase offset varies from sensor tofor the 60 sensors over thesensor. That is, the interference
right hemisphere was calculated using
where each sensor had a different
that was determined bygenerating the uniform random number between 0 and . The

simulated recordings containing this interference are shown in
Fig. 3(b). It should be pointed out that it is difficult in practice
to filter out such periodic interference as that in Fig. 3(a)–(b),because the frequency of the interference is very close to thefrequencies of the signal source activities.
The third type of interference was a linear trend whose inclination varies from channel to channel. That is, was calculated
where each sensor had a different value of.
using
The parameter
was determined by generating the Gaussian
random number whose standard deviation was equal to, whereis the maximum value of. Simulated recordings containing such a linear trend are shown in
Fig. 3(c). The fourth type of interference was a combination ofthis linear trend with a low-frequency noise. In this case,was calculated by using
where
was set at 1.1 Hz and is the same for all sensor
recordings. The simulated recordings containing this interference are shown in Fig. 3(d). It should again be pointed out that
it is in practice difficult to filter out such low-frequency interference because actual MEG signals contain large amounts of
low-frequency components.
was calculated
The covariance matrix of interference, and the total covariancenumerically using
was obtained using. The eigenvalue
matrixspectra offor these four types of interference are shownin Fig. 4. The spectra show that the first and the third interferences have a single large eigenvalue, indicating that theseinterferences are rank-one interferences. The second and theSEKIHARA et al.: PERFORMANCE OF AN MEG ADAPTIVE-BEAMFORMER SOURCE RECONSTRUCTION TECHNIQUE

95

Fig. 3. Simulated magnetic-field recordings containing low-rank interferences. (a) A periodic interference with a frequency of 13.7 Hz was superimposed onto
the recordings of 60 sensors located over the right hemisphere. (b) The same periodic noise, except that the phase offset varying from sensor to sensor, wassuperimposed onto the 60-sensor recordings over the right hemisphere. (c) A linear trend with its inclination varying from sensor to sensor was superimposed onto
all sensor recordings. (d) A combination of the linear trend in (c) with a low-frequency noise of 1.1 Hz was superimposed onto all sensor recordings.

Fig. 4. Eigenvalue spectrum of R shown up to the 40th eigenvalue. (a) The periodic interference in Fig. 3(a). (b) The periodic interference with a random phaseoffset in Fig. 3(b). (c) The linear trend in Fig. 3(c). (d) The linear trend with a low-frequency noise of 1.1 Hz in Fig. 3(d).

fourth interferences have two distinctly large eigenvalues, indicating that they are rank-two interferences. The contour plots ofthe first spatial eigenvectors of the four kinds of interferences

are shown in Fig. 5(b)–(e). The lead field vector of the secondsource is also shown in Fig. 5(a) as a typical lead field from abrain source.

96IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 1, JANUARY 2004

Fig. 5. (a) The contour plot of the lead field vector for the second source, l(r ;  ). (b) The contour plots of the first eigenvector of R . The periodic interference
shown in Fig. 3(a) was applied. (c) The first eigenvector of R . The periodic interference with a random phase offset shown in Fig. 3(b) was applied. (d) The first
eigenvector of R . The linear trend shown in Fig. 3(c) was applied. (e) The first eigenvector of R . The linear trend with a low-frequency noise of 1.1 Hz shown in
Fig. 3(d) was applied. The dots represent locations of sensors. (The locations are slightly distorted.) The anterior, posterior, left and right directions are indicatedby A, P, L, and R, respectively.

Fig. 6. Results of the square root of the average power reconstruction, hs(r ; t) i, obtained from the simulated magnetic-field recordings in Fig. 3. (a) The
simulated magnetic-field recordings in Fig. 3(a) used. (b) Those in Fig. 3(b) used. (c) Those in Fig. 3(c) used. (d) Those in Fig. 3(d) used. The reconstruction was
performed by using (3).

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97

Fig. 7. The source time-course estimates s(r ; t) (where j = 1, 2, and 3) obtained from the simulated magnetic-field recordings in Fig. 3. (a) The simulated
magnetic-field recordings in Fig. 3(a) used. (b) Those in Fig. 3(b) used. (c) Those in Fig. 3(c) used. (d) Those in Fig. 3(d) used. The reconstruction was performedby using (1) and (2).

It can be seen that the spatial eigenvectors for all four cases
are very different from this lead field. The values of the genare less thanfor alleralized cosine
four cases. These very small values of the generalized cosine
confirm our visually obtained interpretation that the eigenvectors in Fig. 5 are very different from the lead field vector of a
was also
brain source. The value of
calculated for the rank-two interferences. This value was on thefor these cases. The generalized cosine between
order ofthe lead field vector and the second eigenvector was less thanfor the cases in Fig. 3(b)–(d). These numerical evaluations suggest that the influence of the interferences should bevery small, according to our analysis in Section III. The beamformer reconstruction was applied to the four cases in Fig. 3.
The results of source power reconstruction are shown in Fig. 6.
The source-activity time courses are shown in Fig. 7. No observable influence exists in any of the results in Figs. 6 and 7. In
the results shown in Fig. 7, the correlation coefficients between
the reconstructed and the original time courses were found to
be greater than 0.99 for all the three time courses in any of thefour cases. These results clearly demonstrate the validity of ouranalysis in Section III.

V. DISCUSSION
In deriving (14), we assume that the power of the interference
is much larger than the power of the sensor noise. Because thepower of the interference is equal to andis approximately equal to(as shown in Appendix), this assumption. When the power of theleads to the conditioninterference is comparable to the power of the sensor noise, thiscondition is not satisfied and (14) should be changed to(29)
The second term of the right-hand side of the above equation
represents the time course of the interference contained in the
beamformer output. The amplitude of this interference timecourse is proportional to.
To evaluate the amplitude, we consider a simple case wherea single source exists. Its lead field vector and its power are denoted as and , respectively. Assuming that the beamformer
is exactly tuned to this source, i.e.,, we can derive

(30)

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where
and
. Therefore, when the lead field vector of a brain source is so different
holds, the amplifrom that the relationshiptude of the interference time course in the beamformer output
is nearly equal to zero. This conclusion can be extended to acase where multiple sources exist and to a case where no source
exists.
is the whiteBecause the square of the weight norm
noise power gain in the beamformer reconstruction process, theis approximately proportional toquantity
the SNR in the beamformer output. This quantity, defined as, is sometimes used for evaluating the statistical significanceof the reconstructed results [3]. The value is expressed as(31)
In a manner similar to deriving (16), we can derive

(32)
where

(33)
and
Therefore, when the assumptions that
hold, the influence of the interference on the value
is also negligible. The value is small when and are very
different because only the numerators in (33) contain the crossproducts of and . In the numerical experiments in Section IV,
is always less thanfor all four interference cases.
The minimum-variance beamformer is known to be very sensitive to errors in the forward modeling or errors in estimating
the measurement covariance matrix [14]. The eigenspace-projection beamformer provides an output SNR higher than that of
the minimum-variance beamformer when such errors exist [15].
, theRedefining the weight vector obtained from (2) as
extension to the eigenspace-projection beamformer is definedas [15]

Therefore, the same discussion as that for (14) can be applied tothis case, leading to the conclusion that the time course estimate
from the eigenspace-projected beamformer is not affectedby the interference.
In summary, we analyzed the influences of additive low-rankinterference on the reconstruction results of MEG adaptive
beamformer techniques. We found that the influence is negligible when the eigenvectors of the covariance matrix obtained
from such interference are very different from any of the leadfield vectors in the source space. The results of our numericalexperiments confirmed this conclusion. The assumptions thatinterference is low rank and its spatial eigenvectors are different
from the lead field of a brain source are generally satisfied formany types of artificial (nonbiological) interference, and theadaptive beamformer techniques are generally robust to theoverlaps of such interference.
These assumptions, however, may not hold for some interference with biological origins. Several investigations havepointed out the possibility that background cortical activities
are caused by a large number of randomly activated sources[16], [17]. Also, some biological interference such as thatcaused by eye blinks or cardiac motions may invalidate thebecause the lead fields
assumption thatfor an eye blink source or a cardiac source may not be very
different from the lead field for a brain source. Therefore,
the analysis presented in this paper cannot generally apply tointerference with biological origins. Thus, methods should be
developed to reduce the influence of such interference, with thepossible application of preprocessing with independent-component-analysis techniques toward these ends [18].
APPENDIX
This appendix derives the relationship. The
assumption to derive it is that any lead field vector in the source
space is so different from the spatial eigenvector of the interference that their generalized cosine is approximately equal
to zero. We first consider a simplest case where a single source
exist whose lead field vector and the power are, respectively, deis expressed as
noted as and . Then,andis expressed as(34)
is a matrix whose column vectors are the eigenvectors
whereof that correspond to the eigenvalues from the signal (and interference). Therefore, using (10), the output of the eigenspaceprojection beamformer is given by(35)
and the eigenvector
Since the source lead field vector
exist in the signal-plus-interference subspace, they areunaffected by the signal-plus-interference-subspace projector, i.e.,
(36)

where
rive

. Thus, using, we de(37)When two sources exist, the power and the lead field vector of
the second source are denoted as and , and a matrix isdefined as. Here, because
is equal
to the covariance matrix for the single-source case presented
holds. We define asabove, the relationship. Usingand, we can finally derive(38)

SEKIHARA et al.: PERFORMANCE OF AN MEG ADAPTIVE-BEAMFORMER SOURCE RECONSTRUCTION TECHNIQUE

It can be shown that the argument presented above is extended
to a case where more than two sources exist.
ACKNOWLEDGMENT
The authors wish to thank Dr. S. Robinson and J. Vrba for
their insightful discussions.
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Kensuke Sekihara received the M.S. degree and
Ph.D. degrees from Tokyo Institute of Technology,
Tokyo, Japan, in 1976 and 1987, respectively.
From 1976 to 2000, he worked with Central
Research Laboratory, Hitachi, Ltd., Tokyo. He wasa visiting Research Scientist at Stanford University,
Stanford, CA, from 1985 to 1986, and at Basic Development, Siemens Medical Engineering, Erlangen,Germany, from 1991 to 1992. From 1996 to 2000,
he worked with the “Mind Articulation” research
project sponsored by Japan Science and Technology
Corporation. He is currently a Professor at the Tokyo Metropolitan Instituteof Technology. His research interests include the neuromagnetic sourcereconstruction, and statistical signal processing, especially its application tofunctional neuroimaging.
Dr. Sekihara is a member of IEEE Medicine and Biology Society and theIEEE Signal Processing Society.

Srikantan S. Nagarajan received the B.S. degree inelectrical engineering from the University of Madras,
Madras, India, and the M.S. and Ph.D. degrees fromthe Department of Biomedical Engineering at Case
Western Reserve University, Cleveland, OH, in 1993
and 1995 respectively.
From 1995–1998, he was a Postdoctoral Fellow
at the Keck Center for Integrative Neuroscience, theUniversity of California, San Francisco (UCSF). In
1999, he was a full-time Research Scientist at Scientific Learning Corporation, Berkeley, CA, and an Adjunct Assistant Professor in the Department of Otolaryngology at UCSF. From
2000–2002, he was an Assistant Professor in the Department of Bioengineering
at the University of Utah, Salt Lake City. Currently, he is the Director of the
Biomagnetic Imaging Laboratory and an Assistant Professor in Residence in the
Department of Radiology at UCSF. His research interests in neural engineering
include multimodal and multiscale functional brain imaging using fMRI, MEG,
EEG, systems and computational neuroscience, neuro-rehabilitation.

David Poeppel received the B.S. and Ph.D degrees
in cognitive neuroscience from the Massachusetts Institute of Technology, Cambridge, in 1990 and 1995
respectively.
He is currently an Associate Professor in the
Departments of Linguistics and Biology at the
University of Maryland at College Park. His researchuses the functional neuroimaging methods magnetoencephalography (MEG), electroencephalography(EEG), positron emission tomography (PET), andfunctional magnetic resonance imaging (fMRI) to
investigate the neural basis of speech and language processing.

Alec Marantz received the B.A. degree in psycholinguistics from Oberlin College, Oberlin, OH, in1978 and the Ph.D. degree in linguistics from the
Massachusetts Institute of Technology (M.I.T.),
Cambridge, in 1981. He joined the faculty at M.I.T.
in 1990, where he is currently the Kenan Sahin
distinguished Professor of Linguistics and Head of
the Department of Linguistics and Philosophy. His
research interests include the syntax and morphology
of natural languages, linguistic universals, and theneurobiology of language. He is currently involved
in revising morphological theory within linguistics and in exploring MEG
techniques to uncover how the brain processes language.