extraction of microsaccade-related signal from single
TRANSCRIPT
ISNN 2010
Extraction of microsaccade-related signal from single-trial localfield potential by ICA with reference
Meng Hu • Hongmiao Zhang • Hualou Liang
Received: 8 March 2010 / Accepted: 18 October 2010 / Published online: 4 November 2010
� Springer-Verlag London Limited 2010
Abstract During visual fixation, we unconsciously make
tiny, involuntary eye movements or ‘microsaccades’,
which have been shown to have a crucial influence on
analysis and perception of our visual environment. Given
the small size and high irregularity of microsaccades, it is a
significant challenge to detect and extract the microsac-
cade-related neural activities. In this work, we present a
novel application of the independent component analysis
with reference algorithm to extract microsaccade-related
neural activity from single-trial local field potential (LFP).
We showed via extensive computer simulations that our
approach can be used to reliably extract microsaccade-
related activity. We then applied our method to real cortical
LFP data collected from multiple visual areas of monkeys
performing a generalized flash suppression task and dem-
onstrated that our approach has excellent performance in
extracting microsaccade-related signal from single-trial
LFP data.
Keywords LFP � Microsaccade � ICA-R
1 Introduction
Our eyes move continually. Even during visual fixation, we
unconsciously make small (generally\1�), involuntary eye
movements or ‘microsaccades’ at an average rate of
1–2 per second. These tiny eye movements, once disre-
garded as oculomotor noise with no useful purpose [1],
have recently received increasing attentions. For instance,
microsaccades are now thought to counteract visual fading
[2] and contribute to discriminate the high spatial fre-
quencies [3]. It has also been observed that microsaccades
modulate neural activities throughout the visual system
[4–10].
However, because of the small size and high irregularity
of microsaccades, it is a significant challenge to extract the
microsaccade-related neural activity from single-trial
recording. In previous studies, microsaccade-related signal
is estimated by simple average to achieve the microsac-
cade-triggered activity [7–9]. This approach, similar to the
traditional event-related potential (ERP) method, assumes
that there are no variations at all in amplitudes, latencies or
waveforms of the evoked potentials across many micro-
saccades. This is a strong assumption and may not be valid
in practice. To overcome this limitation, we apply the
independent component analysis with reference (ICA-R)
algorithm to single-trial LFP for extracting microsaccade-
related signal.
ICA-R algorithm aims to extract desired source signals
from observed mixtures without knowledge of mixing
coefficients [11]. It takes advantage of prior information
about the desired source signal as a reference to guide the
separation process. As a result, the ICA-R algorithm
extracts only the desired source signal, which is the closest
to the reference signal. The ICA-R algorithm has been
successfully used for speech processing, ECG, EEG and
fMRI data analysis [12–15]. In this paper, we use ICA-R to
extract microsaccade-related signal from single-trial LFP,
even with low signal-to-noise ratio (SNR).
The rest of the paper is organized as follows. In Sect. 2,
we describe the neural data used in this paper and ICA-R
algorithm. In Sect. 3, computer simulations are performed
to verify the effectiveness and robustness of our approach.
Our method is then applied to real cortical LFP data
M. Hu � H. Zhang � H. Liang (&)
School of Biomedical Engineering, Science and Health Systems,
Drexel University, Philadelphia, PA 19104, USA
e-mail: [email protected]
123
Neural Comput & Applic (2011) 20:1181–1186
DOI 10.1007/s00521-010-0469-2
collected from monkeys performing a generalized flash
suppression (GFS) task. Section 4 contains the conclusion.
2 Materials and methods
2.1 Experiment and data description
Generalized flash suppression [16, 17], in which a salient
visual stimulus could be rendered invisible despite contin-
uous retinal input, had provided a rare opportunity to study
neural mechanisms directly related to perception. In the GFS
task, monkeys were required to press the lever to initialize a
trial. As soon as a monkey gained fixation, the stimulus of a
red disk (target) was presented. At 1,400 ms after the target
onset, small random-moving dots appeared as the sur-
roundings. With the immediate presence of the surround-
ings, the red disk could be rendered invisible. If the stimulus
disappeared from perception, the monkey was trained to
release a lever; otherwise, monkey was to hold the lever.
Therefore, based on the responses of the animal, the trial was
classified as either ‘‘visible’’ or ‘‘invisible’’. Note that the
stimuli in these two conditions were physically identical.
Multi-electrode local field potential (LFP) recordings
were simultaneously collected from multiple cortical areas
V1, V2 and V4 while monkeys performed the GFS task.
The data were obtained by band-pass filtering the full
bandwidth signal between 1 and 500 Hz, and then resam-
pled at 1,000 Hz. Horizontal and vertical eye positions
were digitized at a sampling rate of 1,000 Hz. Microsac-
cades were detected by our previous developed algorithm
[18]. In this report, we use the LFP neural recordings of
totally 88 channels from area V1 to demonstrate the
effectiveness of our method.
2.2 Independent component analysis with reference
The ICA-R algorithm has been successfully used for signal
analysis and extraction. The goal of the ICA-R is to maxi-
mize the contrast function approximated by negentropy [19]
JðyÞ � k½EfZðyÞg � EfZðgÞg�2, subject to h(w) B 0, where
y ¼ wT �x, w is a weight vector, �x is the pre-whitened
observed signals, k is a positive constant, g is a Gaussian
variable having zero-mean and unity variance, Z(�) is a
nonquadratic function, h(w) is a constraint to the contrast
function indicating the closeness measure. This problem can
be formulated as an augmented Lagrangian function [11]:
Lðw; lÞ ¼ JðyÞ � 1
2s½max
2 flþ shðwÞ; 0g � l2�;
where s is a scalar penalty parameter, l is an initial value
for the Lagrange multiplier. In this paper, we solve the
problem with an efficient implementation of ICA-R [12],
which is used to extract microsaccade-related signal by
pre-whitening the observed signals and normalizing the
weight vector. Here, we provide a brief description of ICA-
R algorithm; more details can be found in [12].
1. Center the observed signals x to make its mean zero;
2. Whiten the observed signals x to give �x;
3. Take a random initial vector w0 of norm 1, or just let
w0 = 0;
4. Choose proper s, l and learning rate g. In this work,
they are set to 0.02, 10.8 and 0.08, respectively;
5. Compute the constant k ¼ jEfZðyÞg � EfZðgÞgj;6. Update the Lagrange multiplier l by lkþ1
maxf0; lk þ shðwkÞg;7. Update the weight vector w by wþkþ1 wk � gL0wk
=
eðwkÞ, where eðwÞ ¼ kEfZ 00ðyÞg � 0:5gEfh00ðwÞg;8. Normalize the weight vector w by wkþ1 wþkþ1
�
wþkþ1
�� ��;
9. Until wTk wkþ1
�� �� approaches 1 (up to a small error),
otherwise go back to the Step (5).
In our application, we use a leave-one-out approach to
obtain the average as a reference. Specifically, all the trials
but the one being considered are used to calculate the
reference signal. The reference signal is obtained by
averaging across trials, then across electrodes.
3 Result
In this section, we perform extensive computer simulations
to verify the effectiveness and robustness of our method,
then apply it to real LFP data.
3.1 Simulations
It has been shown that the characteristic of the microsac-
cade-related signal shows a dominant peak or trough [8]. In
the simulations, we hence use a one-cycle sine wave with
peak-to-peak value of 2 to model the desired target (mi-
crosaccade-related) signal as shown in Fig. 1a.
For the cortical LFP signal, the microsaccade-related
signal is typically inappreciable due to its small size,
especially in the single-trial neural recording. As such, in
our simulation, the simulated microsaccade, i.e., the target
signal, is buried in the background activity, which is sim-
ulated as a mixture of zero-mean white Gaussian noise
e2(n) with variance of 3 and colored noise e1(n) generated
by second-order random AR process [20, 21]:
e1ðnÞ ¼ 0:75e1ðn� 1Þ � 0:35e1ðn� 2Þ þ uðnÞ;
where u(n) is a zero-mean white Gaussian noise with
variance of 0.25. Figure 1b displays an example of
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simulated signal, which is constructed by a simple sum-
mation of the target signal and the simulated background
activity. In the simulation, it is set to 1,000 data samples
with sample rate of 1,000 Hz.
In what follows, we generate 50 realizations of simu-
lated data, each consisting of 20 channels. For each reali-
zation, the scaling factor of the target signal for each
channel is Gaussian distributed with mean of 1 and vari-
ance of 0.2, and the latency shifts across realizations are
uniformly distributed from -10 to 10 ms. Figure 2 shows
the results of a typical realization with -10 ms latency
shift after the ICA-R is applied. The scaling factors in
Fig. 2a–d are respectively 0.7, 1.1, 1.6 and 1.7. From these
results, we can see that the estimated target signal (dash-
dot) matches the true target signal (solid) well in each
panel, especially for the one-cycle sine part, which presents
the most relevant information of target signal.
Figure 3 shows the grand averages of true target signal
(solid) and estimated target signal (dash-dot), which are
obtained by averaging across all trials, then across all
channels. From Fig. 3, we can see that two average wave-
forms match well, especially for their one-cycle sine wave
portions. This result provides further support that our
approach is indeed capable to extract desired signals from
low SNR data. Together, these results demonstrate that our
method not only is able to recover the target signal at the
low SNR, but also works well at different latencies and the
scaling factors.
To quantify the performance of our algorithm, we use
the root mean square error (RMSE) between the true target
Fig. 1 The target signal
(a) and a typical example of
simulated signal (b)
Fig. 2 Simulated results for
-10-ms latency shift: a scaling
factor 0.7, b scaling factor 1.1,
c scaling factor 1.6, and
d scaling factor 1.7
Neural Comput & Applic (2011) 20:1181–1186 1183
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signal s(n) and the estimated target signal s_ðnÞ. The RMSE
is computed as
RMSE ¼ 1
N
XN
n¼1
ðsðnÞ � s_ðnÞÞ2
( )1=2
;
where N is the number of data samples. Our second
measure is the SNR, which is computed as
SNR ¼ 10 log10
PNn¼1 s2ðnÞ
PNn¼1 ðsðnÞ � s
_ðnÞÞ2
( )
ðdBÞ:
Figure 4a shows the RMSE as a function of SNR of
the simulated signal. From this figure, we can see that
when SNR of simulated signal is as low as -20 dB, RMSE
remains quite small (below 0.2), indicating that our
algorithm works well even in the low SNR. Figure 4b
shows the SNR of estimated signal as a function of SNR of
simulated signal. When SNR of simulated signal is -20 dB,
with our algorithm the SNR can be increased to 5 dB. These
results indicate that our algorithm can be used to extract the
desired signal from low SNR signal with different scaling
factors and latency shifts.
3.2 Application to monkey cortical LFP data
The LFP recording consists of data collected from many
sessions, each having many trials. In each trial, there are
a number of microsaccades occurring at different times.
For each microsaccade, multi-electrode LFP data is first
extracted from 50 ms prior to microsaccade onset to 350 ms
after microsaccade onset in each trial of a session. ICA-R is
then performed on these microsaccade-triggered segments to
extract microsaccade-related signal.
To appreciate the effectiveness of our method, we first
apply our approach to LFP recordings before surrounding
onset, in which the data are well controlled except the
microsaccade as the major influence. We then apply our
algorithm to the LFP recordings after surrounding onset,
where we compare the raw microsaccade-triggered signal
with the extracted microsaccade-related signal for both
visible and invisible conditions. The results demonstrate
that the microsaccade-related signal extracted by our
method has much clearer separation of two conditions
than those obtained by the simple microsaccade-triggered
average.
3.2.1 LFP data before surrounding onset
In this section, the microsaccade-triggered averages are
calculated for both raw LFP data and the ICA-R-extracted
LFP. These averages are compared after they are normal-
ized. As shown in the Fig. 5, both averages demonstrate the
consistent trend: LFP shows intensive strong suppression
from about 50 to 200 ms after microsaccade onset, fol-
lowed by a relatively weak suppression. These curves
provide a clear indication of influence of microsaccades on
neural activity.
On the other hand, we can see from Fig. 5 that the
standard error of mean for the extracted microsaccade-
related signal (solid) is smaller than those obtained by the
microsaccade-triggered average (dashed). This result sug-
gests that our method can be used to extract microsaccade-
related component.Fig. 3 Comparison of average of true target signals (solid) and of
estimated target signals (dash-dot)
Fig. 4 RMSE (a) and SNR
(b) of estimated signal as a
function of SNR of simulated
signal
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3.2.2 LFP data after surrounding onset
In this section, our approach is applied to LFP data after
surrounding onset. Figure 6 shows the extracted micro-
saccade-related signal in two conditions, in which there are
two curves that correspond to ‘visible’ (solid) and ‘invisi-
ble’ (dashed) condition, respectively, showing clearly the
microsaccade-modulated neural activity. From Fig. 6, we
can see that immediately after the microsaccade onset,
there is a strong suppression of neural activity for both the
visible and invisible conditions, followed by a clear sepa-
ration of these two conditions from about 90 to 250 ms
before the two curves merged.
In contrast, in Fig. 7, we show the microsaccade-trig-
gered average based on the raw LFP data. In general, there
is a good agreement between Figs. 6 and 7. However, there
are two discrepancies that merit our further comments.
First, the difference of the two conditions in Fig. 6 is sig-
nificantly larger than that in Fig. 7, as shown by statistic
test (p \ 10-8 vs. p \ 10-4), indicating that our method is
able to detect more subtle difference in neural activity
evoked by microsaccades. Second, around the microsac-
cade onset, the difference between two conditions in Fig. 7
disappears in the data obtained by our method, as shown in
Fig. 6. The difference between two conditions in Fig. 7 is
largely related to the separation of perceptual visibility
(visible vs. invisible), whereas in Fig. 6, the extracted LFP
is mostly due to the occurrence of microsaccades, This
discrepancy underscores that our method is able to reliably
extract the microsaccade-related activity.
4 Conclusion
Previous studies showed that the ICA-R has a potential to
extract the desired target signal by choosing a relevant ref-
erence signal. In this paper, we extracted microsaccade-
related signal from single-trial LFP data by the ICA-R algo-
rithm. By simulations, we have shown that our approach can
be used to extract the desired signal in the low SNR signal,
and it is not sensitive to the trial-by-trial variations. These
simulations validated the effectiveness and robustness of our
method. The applications to cortical LFP demonstrated that
our approach has excellent performance in extracting
microsaccade-related signal from single-trial LFP data.
Acknowledgments This work is partially supported by NIH. We
thank Dr Melanie Wilke for proving the data, which were collected at
the laboratory of Dr Nikos Logothetis at Max Planck Institute for
Biological Cybernetics in Germany.
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Fig. 5 Comparison of the ICA-R-extracted microsaccade-related
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