Data Preprocessing

The brain signal is comparatively small than the environmental noises. For signal-to-noise ratio (SNR) enhancement, preprocessing for the recordings is necessary before the further processing [35]. Generally, because the brain signal is usually modeled by ran-dom signals, we repeat the experiment several times to obtain sufficient amount of record-ings. The preprocessing steps we use for MEG recordings are as below statements. First, while conducting experiment, artifacts, body action and eye blinking can induce signifi-cant noises, compared to the real measurement. Hence, we can reduce artifact noise by finding out the abnormal scale of electric ocular graph (EOG) channels. Second, signal space projection (SSP) is often exploited to eliminate the unbalanced noise effect on dif-ferent sensors [36]. SSP is accomplished by calculating individual basis vectors for each term of the functional expansion to create a signal basis covering all measurable signal vectors. By this method, we can transform the interesting signals to virtual sensor config-urations [37]. Third, there are some unavoidable external artifacts, heartbeat, breath and power line noises. The artifact of heartbeat and breath is about one time per second (1 Hz), and power line is 60 Hz and its harmonic. Therefore, we use bandpass filter to ex-clude these artifacts. Moreover, the recordings on each sensors may drift along with time because of the device, so we need to conduct baseline correction. To take mean or peak recordings into analysis, any noise in the baseline will add noise to the input recordings.

We conduct the baseline correction by subtracting a baseline from the recordings. The baseline is usually estimated by the mean of the recordings in the control state period, at which it assumes the recordings are unaffected by the stimulus. Finally, if the activation of interest is time- and phase-locked, according to the central limit theorem, we can eliminate the variance of the recordings contributed by the random noises, in proportion to the square root of trial numbers. We can align each trial of recordings by the onset time and average them synchronously. The all preprocessing steps are shown in Figure 3.4.

Figure 3.4: This graph shows the all preprocessing steps for MEG recordings. For SNR enhancement, preprocessing for the recordings is necessary before the further processing.

First removing artifacts by finding out the abnormal scale of EOG channels. Then elimi-nating the unbalanced noise effect on different sensors by applying SSP. The next step is applying bandpass filter to remove the other artifacts like heartbeat and breath and some environmental noises like power line noises. The next step is to conduct the baseline cor-rection to eliminate the drift of recordings. After the whole process of preprocessing, we can go on for further analysis with enhanced SNR of recordings.

3.3 Statistical Evaluation of the Amount of Recordings

We use statistical analysis described in Chapter 2 to find a reference indicator to show the concept about the amount of recordings. We take the recordings of the left index finger lifting for statistical analysis. After preprocessing mentioned in Section 3.2, we select -350 ms to -200 ms as the control state and 0 ms to 150 ms as the active state. Then we apply paired t-test to the selected control and active states. We test two kinds of the control and active states. The one is after synchronously averaging from every trial of the raw recordings and the other is only the combination of every trial of the raw recordings. After applying paired t-test, we display the p-value under the significance level of 0.05 with increasing number of trials.

We find that the number of trials actually affects the p-value generated fro, applying average recordings of control and active states to paired t-test. The same effect also appears in raw recordings. The results are shown in Figure 3.5 and Figure 3.6. We sort the MEG sensors by their p-values and represents the corresponding p-value of each MEG sensor at the vertical axis. From this figure, we can find out that for both situations when the number of trials increase, the p-value becomes smaller, which also means more significant. Because of this phenomenon, we can set a evaluation criterion that when the number of sensors that reaches some significant level is as large as we expect, the amount of recordings is statistically sufficient.

Figure 3.5: Synchronously averaging recordings with increasing number of trials, for a period of 30 trials. Selecting the control and active states, and then applying the two states to paired t-test. From this figure, we can also find out that the p-value becomes smaller while the number of trials increase.

Figure 3.6: Selecting the control and active states from the raw recordings, without syn-chronously averaging. Then we apply the two states to paired t-test. From this figure, we can find out that the p-value becomes smaller while the number of trials increase.

3.4 Beamformer-based ICA

Following the concept of virtual sensors from beamformer, we can combine Maximum Contrast Beamformer (MCB) and Independent Component Analysis (ICA) as Beamformer-based ICA. We consider filtered signals form the MCB spatial filter as the output from the virtual sensor at each voxel of interest and take them as the ICA input signal. By com-bining ICA with MCB, we can use ICA to separate sources that filtered from MCB spatial filter to get more accurate solution. Using Beamformer-based ICA, we can ignore some inappropriate adjustment of the regularization parameter. Moreover, we can raise the reso-lution of ICA input data using Beamformer-based ICA to reach the purpose of topographic mapping.

When conducting experiments for Beamformer-based ICA evaluation, we take the cor-relation between sources into consideration. While there exists an implicit assumption in beamformer techniques that the time courses of the source activities should be orthogonal to each other; in the other word, all source activities should be completely uncorrelated [38].

We test Beamformer-based ICA for the utility of correlated sources. The experiment results are shown in the following statements.

We conduct the simulation data to validate Beamformer-based ICA. The strength of the two sources is both 30 nAm. Frequencies of the temporal profiles for the two sources are w⁰₁ and w₂⁰, where w⁰₁ is composed of w₁ and w₂, related to a coefficient ξ. We can adjust the correlation between two sources with specified values of ξ. In this simulation data, we set w1 and w2 as 7 Hz and 17 Hz sinusoid signal.

w⁰₁ = (1 − ξ)w₁+ ξw₂ w⁰₂ = w₂

We added background sources with 3000 random dipoles with the standard deviation of 10 nAm. The variances of sensor noises are estimated from the empty room recordings of the MEG system. Taking -500 ms to 0 ms as the control state and 0 ms to 500 ms as the active state, we calculate the MCB spatial filter. Under some specified regularization parameters, we take the filtered signals from MCB spatial filter as the ICA input. The α-significance level is set as 0.05 to extract only target source activities because too many filtered signals

as the ICA input will disturb the optimization. All settings for the simulated recordings is shown in Figure 3.7.

Figure 3.7: (a) the ground truth location in anatomical image of the simulated recordings (b) the temporal profiles of w1 and w2.

The result of Beamformer-based ICA with the regularization parameter of 0.0003 is shown in Table 3.2. If sources are uncorrelated, it can reveal two sources in the MCB F-statistical map. We can further separate sources into two components using Beamformer-based ICA. This effect exists in the situation that two sources are partially correlated. When two sources are fully correlated, the MCB F-statistical map cannot reveal two sources clearly because of correlated source cancellation [15] and Beamformer-based ICA can-not separate sources into two components, wither. But we can find it has a tendency toward two sources.

The result of Beamformer-based ICA when the regularization parameter of 0.003 is shown in Table 3.3. The major difference is that when the regularization parameter is set as 0.003, the MCB F-statistical map can no more reveal two sources as clearly as in Table 3.2.

However, after applying Beamformer-based ICA, we can still separate sources into two components when two sources are uncorrelated and partially correlated, which is similar to the result in Table 3.2.

From the above experiment results, we can see the utility of Beamformer-based ICA.

First, we can ignore some inappropriate adjustment of the regularization parameter.

Sec-Table 3.2: This table shows results of Beamformer-based ICA when the regularization parameter of 0.0003. If sources are uncorrelated, we can separate sources into two com-ponents using Beamformer-based ICA. This effect exists in the situation that two sources are partially correlated. When two sources are fully correlated, we cannot separate sources into two components. But we can find it has a tendency toward two sources.

ξ correlation coefficient

MCB Beamformer-based ICA

0.0 0.0000

0.3 0.3939

0.5 0.7071

Table 3.3: This table shows results of Beamformer-based ICA when the regularization pa-rameter of 0.003. If sources are uncorrelated, we can separate sources into two components using Beamformer-based ICA. This effect exists in the situation that two sources are par-tially correlated. When two sources are fully correlated, we cannot separate sources into two components. But we can find it has a tendency toward two sources.

ξ correlation coefficient

MCB Beamformer-based ICA

0.0 0.0000

0.3 0.3939

0.5 0.7071

ond, we can raise the resolution of ICA input data using Beamformer-based ICA to reach the purpose of topographic mapping. Even with inappropriate regularization parameter, we still can get accurate solution to source localization. Like Table 3.2 and Table 3.3, even if the MCB F-statistical map cannot reveal actual source distribution because of in-appropriate regularization parameters, the topographic distribution of Beamformer-based ICA can reveal more detail information. And Beamformer-based ICA also works with par-tially correlated sources even when MCB fails (Table 3.3). For fully correlated sources, Beamformer-based ICA can separate into two components in temporal activation but fails in tomographic distribution.

3.5 Head Motion Correction

We use three kinds of data to validate the proposed algorithm, SLIM, which is described in Chapter 2.3. We will describe the result using Stabilized Linear Model (SLIM) in the below sections.

3.5.1 Simulations

We simulate the recordings of two sources, front and back, with different head poses.

One head pose is slightly leaning forward than the other. From the spatial profiles of simu-lated recordings, shown in Figure 3.8, we can see the front source of simusimu-lated recordings with head leaning forward is stronger than the back sources. The other is just the opposite.

The strengths of the two sources are both 30 nAm. Frequencies of the two sources are 7 Hz and 10 Hz, respectively. We added background sources with 3000 random dipoles with standard deviation is 5 nAm. The variances of sensor noises is estimated from the empty room recordings of the MEG system.

We set the active state as 0 ms to 500 ms and control state as -500 ms to 0 ms. The value of α is 0.0003 and 0.0008. The result is shown in Figure 3.10 and Figure 3.9. From the result of applying SLIM algorithm and not applying SLIM algorithm, we can see that if we just apply MCB in different head poses will tend to have higher F value in the location of stronger sources (Figure 3.9 (a) and (b)). However, the stronger sources are so ”strong” is because of different head poses, not because of stronger strength–the closer the sources are to the MEG sensors, the stronger the sources are. Using SLIM, we can combine different head poses to solve this problem. From Figure 3.10 (c) and Figure 3.9 (c), we can see that both two sources have almost the same F-value.

From the results, we can see the utility of SLIM in this simulated data.

3.5.2 Phantom

We apply MCB and SLIM with phantom data for comparing the differences of synchronized-averaging with the same head poses and different head poses, and SLIM. Although the dipole strength of phantom data is 100 nAm, in order for reliability of validation, we select

Lean Backward

(a) (c) (e)

Lean Forward

(b) (d) (f)

Figure 3.8: (a) the ground truth location in anatomical image of the simulated recordings (b) the temporal profiles of the two sources (c)(d) the temporal profiles of the simulated recordings (e)(f) the spatial profiles of the simulated recordings during a specific time.

the time period of weaker strength, the time period before the strongest peak, as active time. We compare the localization error of the proposed SLIM methods and synchronized-averaging recordings with the same head poses, all with the same number of trial. We use a bandpass filter with 7.5Hz to 35Hz. Then we set 40 ms to 80 ms as active state and iden-tity as control state. The value of α is set as 0.001. The result is shown in Table 3.4 and Figure 3.11. In Figure 3.11, ’o’ and ’♦’ marks represent SLIM and averaging respectively.

The horizontal axis represents the increasing trial number and the vertical axis represents the localization error in mm.

From Table 3.4 and Figure 3.11, we can see that in the phantom experiment, the error when using SLIM is slightly worse than using synchronized-averaging because the selected active state is too strong to make the effect of SLIM attenuate. But the tendency is similar that when the number of trial increases, localization becomes lower.

Lean Backward

Lean Forward

(a) (b) (c)

SLIM

Figure 3.9: (a) simulated recordings with head leaning forward (b) simulated recordings with head leaning (c) the F-statistical map after applying SLIM algorithm

Lean Backward

Lean Forward

(a) (b) (c)

SLIM

Figure 3.10: (a) simulated recordings with head leaning forward (b) simulated recordings with head leaning (c) the F-statistical map after applying SLIM algorithm

Table 3.4: Localization error evaluation among the SLIM, and synchronized-averaging are listing in the table, showing the mean and standard deviation.

Averaging SLIM

(mm) Mean Std Mean Std

20 trials 5.3624 3.6533 5.0472 4.0128 40 trials 2.8690 2.7068 3.4033 3.1971 60 trials 2.0866 2.0564 3.3481 3.2960 80 trials 1.3868 1.1983 2.4119 2.0286

Figure 3.11: This figure shows the localization error evaluation among the SLIM, and Averaging. SLIM and Averaging have the similar tendency.

3.5.3 Experiment of Gender Discrimination

We also take the recordings of gender discrimination for validation. The visual pathway in the human brain has been well-surveyed. First at the visual area in occipital lobe and then divide into two paths. The upper one is about the perception of actions and the lower one is about objects recognition (Figure 3.12). From the spatial profiles of the recordings (Figure 3.13 and Figure 3.14), the brain activation map is first at occipital lobe, visual area inside the brain. Then passing through the temporal lobe for further recognition work.

The recognition-related brain region is at frontal lobe, but its strength is much weaker than the visual-related activation. In this experiment, we set the subject’s head lean forward for stronger activation in frontal lobe and lean backward for stronger activation in occipital lobe with the same experiment paradigm. From the spatial profiles we can see such phenomena actually exists. After applying SLIM algorithm, both frontal and temporal or occipital activation appeared in the F-statistical map (Figure 3.13 and Figure 3.14). For simplicity, we call the head pose of leaning backward as pose 1 and the head pose of leaning forward as pose 2 in the later statements.

Figure 3.12: This figure shows the visual pathway. Starting at the occipital visual area inside the brain and then separating into two paths about perception of actions and objects recognition.

In order to recognize the source location within the time period of interest, we select

the time with 103 ms in occipital area for vision and 139 ms in temporal area for objects recognition. The waveform and topography is shown in Figure 3.13 and Figure 3.14. The active state is set as a period of 40 ms with the time of interest, and the control state is set as 800 ms to 1000 ms or the empty room measurement. The value of α is set as 0.003.

Table 3.5: The results of MCB and SLIM with different head poses and the control state is set as 800 ms to 1000 ms. We can see that the higher F-value of pose 1 at 103 ms is strengthened after applying SLIM.

Pose F-statistical Map at 103 ms F-statistical Map at 139 ms

Lean Backward

Lean Forward

SLIM

From the result, the proposed SLIM algorithm can correct the inaccurate source lo-calization caused by head motion. Furthermore, by combining the different head poses, we can virtually increase the sensor number of MCB model and gmore accurate source

Table 3.6: The results of MCB and SLIM with different head poses and the control state is set as the empty room recordings.

Pose F-statistical Map at 103 ms F-statistical Map at 139 ms

Lean Backward

Lean Forward

SLIM

localization result to reach the gaol of super resolution.

103139

Figure 3.13: The topography and waveform of the pose of leaning backward.

103139

Figure 3.14: The topography and waveform of the pose of leaning forward.

Discussion

In this chapter, we discuss some points we discovered while we conducted research. In-cluding (1) the parameters in Maximum Contrast Beamformer (MCB), (2) practical Issues of Beamformer-based Independent Component Analysis and (3) the sensor number issue of MEG.