IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 53, NO. 9, SEPTEMBER 2006

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A Novel Adaptive Beamformer for MEG Source
Reconstruction Effective When Large
Background Brain Activities Exist
Kensuke Sekihara*, Senior Member, IEEE, Kenneth E. Hild, II, Senior Member, IEEE, andSrikantan S. Nagarajan, Member, IEEE

Abstract—This paper proposes a novel prewhitening eigenspace
beamformer suitable for magnetoencephalogram (MEG) sourcereconstruction when large background brain activities exist. The
prerequisite for the method is that control-state measurements,
which contain only the contributions from the background interference, be available, and that the covariance matrix of the
background interference can be obtained from such control-statemeasurements. The proposed method then uses this interference
covariance matrix to remove the influence of the interference inthe reconstruction obtained from the target measurements. A
numerical example, as well as applications to two types of MEG
data, demonstrates the effectiveness of the proposed method.
Index Terms—Adaptive beamforming, brain noise, magnetoencephalography, prewhitening, source reconstruction.

I. INTRODUCTIONONE MAJOR problem with magnetoencephalogram(MEG) measurements is that measured MEG signal
generally contains interfering magnetic fields generated fromspontaneous brain activities. Such background interference degrades the quality of the source reconstruction results, and often
make interpreting the reconstruction results difficult. Therefore,
the background interference is sometimes referred to as brain
noise or physiological noise. The degradation is particularly
severe in adaptive beamformer source reconstruction methods[1], [2] because the high-rank nature of the background spontaneous activity [3], [4] may invalidate the underlying low-rank
signal assumption necessary for formulating the adaptive
beamformers. We show in Section III that the background brain
activity can cause a significant reduction in the source intensity
and severe spatial blur in adaptive-beamformer reconstruction
results.
This paper proposes a novel prewhitening eigenspace beamformer, which can attain the source reconstruction free from theinfluence of background interference when a large amount ofManuscript received August 10, 2005; revised December 11, 2005. The workof K. Sekihara was supported in part by the Ministry of Education, Science,
Culture and Sports in Japan under Grant-in-Aid C13680948 and Grant-in-Aid
C16500296). The work of S. Nagarajan was supported in part by the Whitaker
Foundation and in part the National Institute of Health (NIH) under Grant
P41RR12553-03 and Grant R01-DC004855-01A1. Asterisk indicates corresponding author.
*K. Sekihara is with the Department of Systems Design and Engineering,Tokyo Metropolitan University, Asahigaoka 6-6, Hino, Tokyo 191-0065, Japan(e-mail: ksekiha@cc.tmit.ac.jp).
K. E. Hild, II and S. S. Nagarajan are with Department of Radiology, University of California, San Francisco, CA 94143 USA.
Digital Object Identifier 10.1109/TBME.2006.878119

background activity exists. The prerequisite for the proposed
method is that control-state measurements, which contain only
the contributions from the background interference, be available, and that the covariance matrix of the background interference can be obtained from such control-state measurements.
The proposed method then uses this interference covariance matrix to remove the influence of the interference in the reconstruction results obtained from the target measurements where bothsignal and interference exist.
The proposed beamformer is particularly useful for reconstructing source activities that are stimulus-evoked but not
time-locked to the stimulus. Since signals from such nontime-locked activities are generally averaged out through theepoch-averaging process, the beamformer weight should be derived using a covariance matrix obtained from nonaveraged raw
epochs. However, the nonaveraged epochs generally containa large amount of background interference whose amplitudeis usually considerably larger than that of the evoked activity.
Therefore, the successful reconstruction of nontime-locked
activities requires removing the influence of the backgroundinterference. In Section IV-B, we show one such example inwhich primary hand-motor activation is clearly reconstructed asa result of applying the method to the motor-evoked field witha frequency band of 15–25 Hz. The result of this application
demonstrates the effectiveness of the proposed method forreconstructing MEG source activities using nonaveraged raw
epochs.
In this paper, we first present the analysis regarding theinfluence of the background interference on the adaptive
beamformer source reconstruction in Section III. Then, theprewhitening eigenspace beamformer is proposed in Section IV.
The proposed method is validated first by our computer simulation in Section V and then by applications to auditory andmotor responses in Section VI. Throughout this paper, plain
italics indicate scalars, lower-case boldface italics indicate
vectors, and upper-case boldface italics indicate matrices. The
eigenvalues are numbered in decreasing order.
II. ADAPTIVE-BEAMFORMER FOR NEUROMAGNETIC
RECONSTRUCTION
A. Definitionsth
We define the magnetic field measured by thedetector coil at timeas
, and a column vector
as a set of measured data0018-9294/$20.00 © 2006 IEEE

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whereis the total number of detector coils and superscript
indicates the matrix transpose. The spatial location is repre.
sented by a three-dimensional (3-D) vector
The covariance matrix of the measurement is denoted as ,where
indicates the ensemble average,i.e.,which is replaced with the time average over a certain time
window in practice. The moment magnitude of a source atis denoted as. The orientation of the source at is
whose
defined as a 3-D vector
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; theoutput is induced by a unit-magnitude source located at andis defined
directed in the direction. The column vectoras. The lead field matrix,
which represents the sensitivity of the whole sensor array at, is defined as. The lead-field
where
vector in the source-moment direction is defined as.
B. Adaptive Beamformer Source Reconstruction
To solve neuromagnetic source reconstruction problems, we
focus on the class of methods referred to as the adaptive beamformer, which was originally developed in the field of arraysignal processing [5]. The beamformer estimates the source curwhereisrent density by computing
exthe estimated source magnitude. The column vector
presses a set of filter weights. The weight vector of the minimum-variance beamformer, which is the best-known adaptive
beamformer, is expressed as(1)
1. Here,where
is defined asisthe optimum direction determined as the direction that gives the
maximum beamformer outputs [7], [8]. Using the above weight,
the reconstructed source power is expressed as(2)
becauseThe minimum-variance beamformer can be extended to theeigenspace-projection beamformer, which is known to be tolerant of errors in the forward modeling or the estimation of thedata covariance matrix [9]. The extension is attained by projecting the weight vector in (1) onto the signal subspace of themeasurement covariance matrix. That is, redefining the weight, the weight vector for the eigenspacevector in (1) as
projection beamformer is obtained using

In this equation,
is a matrix whose columns consist of theis the projection masignal-level eigenvectors of , andtrix that projects a vector onto the signal subspace of .
III. INFLUENCE OF BACKGROUND BRAIN ACTIVITY ON
ADAPTIVE-BEAMFORMER RECONSTRUCTION
We use a model for the measurements

expressed as
(4)

where
is the magnetic field generated from the signal
is the magnetic field generated by thesources of interest,is the additive sensor noise. The
background activity, andspatial-filter outputs are then expressed as(5)
For nonadaptive spatial filters, the influence of the interferenceis simply the overlap of
onto the reconstruc. For adaptive beamtion of the signal of interest,
affects the source reformers, however, the interference
construction results in a more complex manner because
also affects the beamformer weight
through the covariance matrix . In this section, we derive the resolution kernelof the minimum-variance beamformer, taking the backgroundinterference into account. Numerical examples of the resolution kernel are presented in Section V-A. These numerically-obtained kernels clearly show that the background activity cancause a significant source-intensity reduction as well as severe
spatial blur in the adaptive-beamformer reconstruction results.
We define the background interference activity at the locationand time as, and assume that the background sources
are continuously distributed. Thus, we have

(6)
where the integral is taken over the whole source space. Let us
also assume that only a single target source exists at with anorientation equal to . The magnitude of the target source is. Then, defining such that, thedenotedis expressed asmeasurement(7)
can be modeled as white Gaussian noise
The sensor noise
uncorrelated between different sensor channels, and we can genholds
erally assume that the relationshipwhere is the variance of the sensor noise and is the identity
matrix. Therefore, the covariance matrix of the measurements
is given by(3)
1In practice, the normalized lead field l (r )=kll(r )k is often used in (1) to avoid
artifacts caused by the variation of the lead field norm kll(r )k [6]. We use thenormalized lead field in our experiments in Sections V and VI.

(8)

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where the signal power is defined such that.
We also assume that the background source activity is spatially
uniform and incoherent, i.e.,

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and

(16)
(9)

Then, corresponding to (4), the relationshipwhere
is the power of the background source activity. Substituting (9) into (8), we obtain
(10)
where

is the gram matrix defined as(17)
holds whereis the noise matrix defined as.
We define the covariance matrix of the signal magnetic field
generated from the target sources only as , such that(11)
The resolution kernel of the minimum-variance beamformer
for a point source at is expressed as [6](18)We also define the signal-plus-sensor-noise covariance matrix, such that

(12)
Therefore, substituting (10) into (12), we can finally derive theexplicit form of the kernel such that(19)
and the interference-plus-sensor-noise covariance matrix
such that

,

(13)
(20)
where
and
.
In (13), the normalized lead field vector is used as andthe explicit notation ofis omitted for simplicity. The
is defined such thatgeneralized cosine in the metric. In
Section V-A, we present numerical examples of the resolution
kernel obtained using (13). These numerical examples showthat when large background activities exist, significant reduction in source intensity, as well as the subsequent degradationof the spatial resolution, arises in source reconstruction results.
IV. PROPOSED PREWHITENING EIGENSPACE BEAMFORMER
A. Definitions
Here, we present the proposed eigenspace beamformer,
which can attain the source reconstruction free from the influence of background interference. To describe the method, we
first make several definitions. We define the spatio-temporalas such thatmatrix of the measurement

We further assume that the background interferences are uncorrelated with the target activity. Under this assumption, therelationship(21)
holds. The fundamental assumption in this paper is that controlstate measurements, which contain only the contributions fromthe background interference and sensor noise, are available, andcan be obthe interference-plus-noise covariance matrix
tained from such control-state measurements. Under this assumption, we have developed a novel beamformer method, theprewhitening eigenspace beamformer, to extract the target activities from the background interference.
B. Prewhitening Eigenspace Beamformer
The proposed beamformer uses the prewhitened measurement covariance matrix , which is defined as. Thus, from (21), we have the relationship

(14)
where
indicate the time points at which themeasurements are performed. The spatio-temporal matrices forandare defined in exactly the same manner as in(14), i.e.,
(15)

(22)
We define the eigenvalues and eigenvectors of asand. Because we assume thattarget sources
exist, according to (22), the largest eigenvalues
are greater than 1 and associated with the signal part; and the other eigenvalues

1758IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 53, NO. 9, SEPTEMBER 2006

are equal to 1 and are associated with the interference and noise
part. That is, is expressed as(23)
and, thus, we have(24)
asUsing these signal-level eigenvectors, we define a matrix, and calculate, which is the projection matrix that project vectors onto the signal subspace of .
Thus, a reasonable estimate of the signal-only covariance matrix, , can be obtained using(25)
An estimate of the signal-plus-sensor-noise covariance matrix,, can be obtained from

Fig. 1. The coordinate system used in the numerical experiments. The coordinate origin was set at the center of the sensor coil located at the center of thearray. The plane at x = 0 cm is shown. The coordinate of the upper left, theupper right, and the lower sources are (0, 1, 6), (0, 1, 6), and (0, 1.6,
7.2) cm, respectively. The circle indicates the boundary of the sphere used forthe forward calculations. The center of the sphere was set to (0, 0, 12).

0 0

0

0

0

0

Thus, we can extract the spatio-temporal matrix of the signal
such thatmagnetic field
(31)

(26)
where is the regularization constant that should be set close
to the variance of the sensor noise . The source power reconstruction free from the influence of the background activity canbe obtained from(27)
A reasonable estimate of the spatio-temporal matrix of thesignal magnetic field
can also be obtained in the sameismanner as described above. The prewhitened version ofdefined as such that

Definingsuch that
relationship,, we have the(32)
and the weight vector of the prewhitening eigenspace beamformer is expressed as(33)
and the interference-free spatio-temporal source reconstruction
is obtained using this, i.e.,(28)
The singular value decomposition of theis expressed as

(29)
(34)
indicates the th temporal singular vector. Here,
whereagain, the first singular values are greater than 1 and they areassociated with the signal part
. The other singularvalues are close to 1 and they are associated with the interference and noise part
. Therefore, by applying
to , we havethe projector(30)

V. NUMERICAL EXPERIMENTS
A. Numerical Examples of Resolution Kernel
A sensor alignment of the 148-sensor array from Magnes
2500 (4D Neuroimaging Inc., San Diego) neuromagnetometeris used in our experiments. Three signal sources were assumed
to exist on a single plane. The source-sensor configuration and the coordinate system are illustrated in Fig. 1,
and the spherical homogeneous conductor model is used for theSEKIHARA et al.: NOVEL ADAPTIVE BEAMFORMER FOR MEG SOURCE RECONSTRUCTION

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p 0 0

Fig. 2. (a) Resolution kernels of the upper-left source located at (0, 1, 6) cm. Five values of  were used:  = 0,  = 0:05 ,  = 0:1 ,  = 0:2 ,and  = 0:5 . The SSNR, which is defined as ( f )=( M ), was set to 2. (b) Plot of the peak value of the kernel, (r ; r ) = f D f , with respectto  for three SSNR values. (c) The same resolution kernels as shown in (a) in which each kernel is normalized with its peak value. (d) Plot of the FWHM of theresolution kernel with respect to  for three SSNR values.

kk

forward calculation. We here assume that only the upper-leftsource is active; the source is located 6 cm below the centerof the sensor array. We calculated theresolution kernel using (13) for five values of. Here,the signal-to-sensor-noise ratio (SSNR), which is defined as, was set equal to 2. Also, in this calculation,
the gram matrix is approximated as

its peak value. These normalized kernels clearly show that the
full-width at half-maximum (FWHM) of the kernels becomes
greater when is increased. The FWHM of the resolution kernels is plotted with respect tofor three different valuesof the SSNR. The results show that, compared to a case where
background interferences are negligibly small, a large spatial
blur can be caused by background activities such as those with.
B. Source Reconstruction Experiments

where
and
are the lead field vectors in the directions of the two tangential components, andis the coordinate of the th voxel. Here, the voxel grid has 0.5-cm interval
within a volume defined as
,
, and
.
The results plotted in Fig. 2(a) show that, when the power ofthe background activity, , is increased, the reconstructed intensity of the source rapidly decreases. The peak value of theresolution kernel
was plotted with respect toin Fig. 2(b) for the three values of SSNR. Theseplots show that large background activities such as those withcan cause a more than 70% decrease in the reconstructed intensity, and that this decrease is more significant when
the SSNR is greater. The same resolution kernels in Fig. 2(a)are plotted in Fig. 2(c) where each kernel was normalized withWe then performed source reconstruction experiments to validate the effectiveness of the prewhitening beamformer proposed
in Section IV. Simulated magnetic recordings were calculated
from 1200 to 1200 time points by assigning the three timecourses shown in Fig. 3(a) to the three sources. We use the spherically homogeneous conductor model [10] for the forward calculation. In these numerical experiments, we consider the data
portion between 1200 and 0 to be the prestimulus period andthat between 0 and 1200 to be the poststimulus period. A small
amount of white Gaussian noise that simulates the sensor noise
was added to the generated recordings, resulting in a SSNR
equal to 12, where the SSNR is estimated using the ratio between the Frobenius norms of the signal and noise matrices, i.e.,. The generated magnetic recordings
areshown in the upper panel of Fig. 3(b). We then generated themagnetic field due to the background interference. In this1760

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Fig. 3. (a) Waveforms of the three sources assumed for the numerical experiments. The waveforms in the top to the bottom panels were assigned to the first to
third sources, respectively. (b) Generated magnetic recordings obtained when no background sources exist (upper panel), and when 100 background sources exist(lower panel).

Fig. 4. Results of the power reconstruction hs(r ; t) i. (a) Conventional eigenspace beamformer was applied to the recordings with no background interference.
(b) Conventional eigenspace beamformer was applied to the recordings with background interference. (c) Prewhitening beamformer reconstruction [see (27)] wasapplied to the recordings with background interference. In these results, the reconstruction grid has 0.1-cm intervals in the y and z directions.

generation, 100 background sources with random locations andorientations had the same power and random time courses. The
background magnetic field
was added toand the resultant simulated magnetic recordings are shown in the lower
panel of Fig. 3(b). Here, the resultant interference-to-signal ratio
was set equal to 2.
The conventional eigenspace beamformer mentioned in
Section II-B was first applied to these two sets of simulated
recordings in Fig. 3(b). Here,was obtained using thewhole poststimulus period, and (2) was used to obtain thesource-power reconstruction. Fig. 4(a) shows theresults for the case with no background interference, andFig. 4(b) shows the results for the case with the backgroundinterference present. Here, the comparison between these two
sets of results again confirms that the background interference
causes a severe blur in the reconstruction results. We thenapplied the prewhitening beamformer in (27) to the data withthe background interference. The results are shown in Fig. 4(c).

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Fig. 5. (a) Averaged auditory-evoked field measured using the 275-channel sensor array. Among the 275 sensor recordings, the recordings from 132 sensors
covering the subject’s left hemisphere are displayed. Two vertical broken lines indicate the time instants 44 and 90 ms. (b) The source reconstruction results
obtained using the conventional eigenspace beamformer. (c) Those from the proposed prewhitening beamformer. The left, middle, and right columns show the
maximum intensity projections of the 3-D reconstruction onto the axial, coronal, and sagittal planes, respectively. The upper case letters L and R show the left andthe right hemispheres, respectively. The upper and lower panels indicate the reconstruction results at 44 and 90 ms, respectively. In these reconstruction results,
the reconstruction grid has 0.5-cm intervals in the x, y , and z directions.

In this application,
was obtained using the whole prestimulus period. In the results in Fig. 4(c), the blur due to the background activity is significantly reduced, and these results clearly
demonstrate the effectiveness of the proposed beamformer.
VI. EXPERIMENTS
We applied the proposed prewhitening beamformer totwo sets of MEG data, measured using the 275-channel

Omega-275 (VSM MedTech Ltd., Port Coquitlam, BC, Canada)
whole-cortex biomagnetometer installed at the Biomagnetic
Imaging Laboratory, University of California, San Francisco.
The first data set is the auditory evoked response, and weapplied the proposed prewhitening beamformer to demonstrate
its capability of spatio-temporal reconstruction free from theinfluence of background interference. The second data set is the
movement-related desynchronization induced by button-press

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Fig. 6. (a) The power spectra P (f ) and P (f ) for the frequency band between 15 and 25 Hz. P (f ) is indicated by the broken line and P (f ) by the solid line.
(b) The maximum-intensity projection of the power reconstruction hs(r ; t) i obtained using the prewhitening beamformer in (27). (c) The MRI overlay of thereconstruction results in (b).

finger movements, and we show that the method can reconstructa clear, localized activity near the hand-motor area, demonstrating that the proposed method is effective for reconstructing
nontime-locked brain activities.
A. Application to Auditory-Evoked Data
The auditory-evoked field was measured with a 1-kHz puretone presented to the subject’s right ear. The average inter-stimulus interval was 2 s, with the interval randomly varied between
1.75 and 2.25 s. The sampling frequency was set at 4 kHz, andan on-line filter with a bandwidth from 1 to 2 kHz was used. A
total of 400 epochs were measured and averaged to produce theaveraged auditory recordings shown in Fig. 5(a). Here, although
clear P50m and N100m peaks can be observed, we can seethat these averaged recordings contain a considerable amountof quasi-periodic background activity.
The reconstruction experiments were performed using theconventional eigenspace-projected beamformer and the proposed prewhitening beamformer. In these experiments, the left
hemisphere was reconstructed using the averaged recordings
from 132 sensors covering the left hemisphere. [Only therecordings from these 132 sensors are displayed in Fig. 5(a).]A portion of the averaged recordings between 0 to 200 ms wasused to estimate the measurement covariance matrix , and theinterference-plus-noise covariance
was obtained from thewhole prestimulus portion between 400 and 0 ms. Two time
points, 44 and 90 ms, are selected for the result comparison.
These time points are shown in the two vertical broken lines inFig. 5(a), and as indicated, one is near the peak vertex of P50m
and the other is near the peak vertex of N100m.
The conventional eigenspace-projected beamformer in (1)and (3) was first applied to these averaged recordings. The
source reconstruction results at the two time points are shownin Fig. 5(b). The results from the prewhitening beamformer,
obtained using (34), are shown in Fig. 5(c). The dimension of
the signal subspace was set to 2 for the both cases. At 90–ms
latency, which is close to the peak vertex of N100m, bothmethods can reconstruct a clear localized source in the left
temporal lobe probably near the primary auditory area. However, at 44 ms, the reconstruction results of the conventional
eigenspace beamformer contain a strong diffuse source, probably caused by the background brain activity. The results fromthe prewhitening beamformer are free from this diffuse source
and clearly detect a localized source in the left temporal lobe,
demonstrating the effectiveness of the proposed prewhitening
beamformer.
B. Application to Movement-Related Desynchronization Data
Here, a subject was asked to press a button with his rightindex finger every 3–4 s. The onset of movement was indicatedby a button press and defined as the time-origin. MEG data
for200 button presses were continuously acquired at a 1 kHz
sampling rate. Because movement-induced magnetic fields are
not precisely phase locked to the movement, we estimated thecovariance matrices from the raw epoched data. Since, the raw
epoch data will be contaminated by background interferences,

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Fig. 7. Comparison between the point spread functions in (36) and (37). The solid lines indicate the point spread function in (36) and the broken lines indicatein (37) were set equal. (a) These values were set to 1, and (b) 0.5. (c) Plot of cos(l ; f ) (solid line) andthat in (37). The value of in (36) and the value ofy 1 cm.
cos(l; f G ) (broken line). These generalized cosines were calculated on the line x = 0, z = 6 and 1

j0

we applied our proposed prewhitening beamformer. It is wellknown that the spectrum of the magnetic field decreases in thebeta-band (15–25 Hz) preceding movement [11]. Therefore, covariance estimates were obtained in the frequency domain.
We set two time windows for covariance matrix estimation:
the first from 1200 to 600 ms, and the second from 600
to 0 ms, both preceding the button press. Fourier transforms ofthe th nonaveraged epoch data in the first and the second time
windows are, respectively, denotedand, and thefrequency-domain sample covariance matrices for the first andthe second time windows,
and , are obtained using

(35)
where
and 2. In this equation, the notation
indicates the summation over a specific frequency band, andwas set to the -band region between 15 and 25 Hz in our experiments. The power spectra averaged across channels,and, were also calculated for the first and the second time windows such thatwhere,
2. The power spectrum
for the frequency bandis plotted by the broken line andby the solidline in Fig. 6(a). These plots indicate thatis larger thanin this frequency band, confirming the movement-related
desynchronization. Consequently,
is used as the target covariance matrix, andas the interference-plus-noise covariance matrix.
We applied the prewhitening beamformer to obtain the source
power reconstruction. The reconstruction results areshown in Fig. 6(b). We can see that the proposed method reconstructs a clear, localized source in the left temporal region. The

0  

MRI overlay of the results in Fig. 6(b) is shown in Fig. 6(c). The
overlay shows that the center of the reconstructed activity is located in contralateral hand-motor cortex. The results in Fig. 6(b)and (c) demonstrate the capability of the proposed beamformer
to successfully reconstruct the nontime-locked source activity
by eliminating the influence of background interference.

VII. DISCUSSION AND CONCLUSION
The analysis and numerical experiments in Sections III and
V-A show that the background interference causes blurred reconstruction. On the other hand, the sensor noise is known tocause the degradation in the spatial resolution [12]. Let us compare the effects of these two types of noise on the spatial resolution. When the background interference is negligibly small,into (12), we derive the kernel insubstituting (10) withthis case as

(36)
where

is defined such that, andis denoted. The SSNR is expressedusing as. In (36), a multiplicative constant is omitted
and the peak value is normalized to 1. When the power ofbackground interference is much larger than the power of
into (13), we derivesensor noise, substituting

(37)

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where
is defined such that
. We
, and adefine the signal-to-interference ratio (SIR) as
multiplicative constant is again omitted in (37).
The results of plotting the point spread functions in (36) andin(37) are shown in Fig.7(a) and (b). Here, in (36) and(37) were set equal; these values were set to 1 in Fig.7(a) and to
0.5 in Fig.7(b). These calculated results show that the FWHM
of the point spread function in (36) is approximately twofold
greater than that for the point spread function in (37). Thatis, the blur caused by the sensor noise is twofold greater thanthat caused by the interference. The difference between thetwo point spread functions is caused by the difference between
and. The decay properties of thesegeneralized cosines are shown in Fig. 7(c), and we can see thatdecays twice as fast as, thus explaining
the difference in these two types of point spread functions.
In summary, this paper proposes a novel prewhitening beamformer, which can achieve source reconstruction free from theinfluence of background brain activities. The prerequisite for the
method is that control-state measurements, which contain only
the contributions from the background interference, be available, and that the covariance matrix of the background interference can be obtained from such control-state measurements.
The proposed method uses this interference covariance matrix
to suppress the influence of the interference in the source reconstruction results. The proposed method is validated by our
computer simulation, as well as by applications to two kinds of
MEG data.
ACKNOWLEDGMENT
The authors wish to thank Sarang S. Dalal for his software
support.
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Kensuke Sekihara (M’88–SM’06) received the
M.S. and Ph.D. degrees from the Tokyo Instituteof 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 “Mind Articulation” research
project sponsored by Japan Science and Technology Corporation. From 2000
to 2005, he was a Professor at Department of Engineering, Tokyo Metropolitan
Institute of Technology, Tokyo. Since 2006, he has been a Professor with the
Department of Systems Design & Engineering, Tokyo Metropolitan University, Tokyo, Japan. His research interests include the neuromagnetic sourcereconstruction, and statistical signal processing, especially its application tofunctional neuroimaging.
Dr. Sekihara is a senior member of the IEEE Medicine and Biology Society
and the IEEE Signal Processing Society. He is an associate editor for IEEE
TRANSACTIONS ON BIOMEDICAL ENGINEERING.

Kenneth E. Hild, II (M’90–SM’05) received the
B.S. and M.Sc. degrees in electrical engineering,with emphasis in signal processing, communications,and controls, from The University of Oklahoma,
Norman, in 1992 and 1996, respectively. He received
the Ph.D. degree in electrical engineering from The
University of Florida, Gainesville, in 2003, where
he studied information theoretic learning and blindsource separation in the Computational NeuroEngineering Laboratory. He has also studied biomedical
informatics at Stanford University, Palo Alto, CA.
From 1995 to 1999, he was with Seagate Technologies, Inc., Scotts Valley,
CA, where he served as an Advisory Development Engineer in the Advanced
Concepts group. From 2000 to 2003, he taught several graduate-level classes on
adaptive filter theory and stochastic processes at the University of Florida. He iscurrently with the Biomagnetic Imaging Laboratory, Department of Radiology,
University of California at San Francisco, where he is applying variational
Bayesian techniques for biomedical signal processing of encephalographic andcardiographic data.
Dr. Hild is a member of Tau Beta Pi, Eta Kappa Nu, and the International
Society for Brain Electromagnetic Topography.

Srikantan S. Nagarajan (S’90–M’96) began his research career at the Applied Neural Control Laboratory, Case Western Reserve University (CWRU),
Cleveland, OH, where he received the M.S. and Ph.D.
degrees in biomedical engineering.
After graduate school, he did a postdoctoral
fellowship at the Keck Center for Integrative Neuroscience, University of California, San Francisco,under the mentorship of Dr. M. Merzenich and Dr.
C. Schreiner. Subsequently, he was a tenure-track
faculty member in the Department of Bioengineering, University of Utah, Salt Lake City. Currently, he is the Director of
the Biomagnetic Imaging Laboratory, an Associate Professor in Residence inthe Department of Radiology, and a member in the UCSF/UCB Joint Graduate
Program in Bioengineering. His research interests are in the area of NeuralEngineering where his goal is to better understand dynamics of brain networks
involved in processing, and learning, of complex human behaviors such as
speech, through the development of functional brain imaging technologies.