Sensor Number Issue of MEG

We may consider that the resolution of the solution to the MEG inverse problem can be improved by increasing the number of MEG sensors. However, this is only correct to the recordings with only uncorrelated noises. With only uncorrelated noises, the accuracy of Equivalent Current Dipole (ECD) reconstruction is improved inverse proportionally to the square root of the sensor number. Once the correlated noises exist, the inter-channel separation is comparable to the brain noise correlation distance and increasing the sensor number does no help. The correlation distance is defined as a distance along the scalp at which the correlation coefficient is reduced to 0.5 [27]. In [26, 27], they demonstrate this phenomenon with ECD reconstruction. They simulate the MEG recordings with different sensor numbers for ECD source localization and the localization error is no more improved above some number of channels.

The above phenomenon is different to beamformer. The spatial filter of beamformer

Table 4.1: The result of Beamformer-based ICA when the regularization parameter of 0.03. Because of very inappropriate regularization parameter, both results of MCB and Beamformer-base ICA cannot reveal actual two sources.

ξ correlation coefficient

MCB Beamformer-based ICA

0.0 0.0000

0.3 0.3939

0.5 0.7071

exploits the correlation between sources to minimize the output variance by canceling the correlated portion of the source of interest [15]. Therefore, the beamformers can remove most of the correlated noises, that is, beamformers are affected only by uncorrelated noises.

Therefore, the performance of beamformers is not limited with the number of sensors.

In [26, 27], they also simulate MEG recordings with increasing sensor number, from 75 to 2000. Applying Synthetic Aperture magnetometry (SAM) [16], the significantly larger sensor number is still beneficial. As a result, the MEG system can benefit from significantly larger number of sensors while applying beamformers.

From above statements, the utility of Stabilized Linear Model (SLIM), described in Chap 2.3, is more remarkable. Applying SLIM, we can conceptually increase the sen-sor number by combining MEG recordings with different head poses. Moreover, we can actually improve the accuracy of Maximum Contract Beamformer (MCB) localization by increasing sensor numbers that the sensor number can be very large. Therefore, we can im-prove the accuracy of MCB localization by combining MEG recordings of different poses.

Conclusions

In 2.1, we propose a method that can reveal the amount of recordings. We apply the statistical hypothesis to the selected control and active states from MEG recordings and examine how the discrimination between two states variate as the number of recordings in-crease. By showing corresponding p-values of each sensor, we can find out some concepts about the amount of recordings.

In 2.2, we combine Maximum Contrast Beamformer (MCB) and Independent Compo-nent Analysis (ICA) as Beamformer-based ICA following the concept of virtual sensors from beamformer. 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 signals.

There are some advantages of Beamformer-based ICA. We can use ICA for MCB filtered source separation to get more accurate solution even with some inappropriate regularization parameters of beamformer. Furthermore, with the concept of virtual sensors from beam-former, we can raise the ICA resolution of topography distribution in sensor space to the resolution of tomography distribution in source space.

In 2.3, we apply Stabilized Linear Model (SLIM) into MCB. By combining record-ings of different head poses, we can not only reduce the error induced from head motion but simultaneously improve the accuracy of source localization by conceptually increasing sensor numbers.

In Chapter 4, the simulation, phantom and real experiment data are used to validate and demonstrate the proposed algorithm. For statistical evaluation of the amount of record-ings, from the p-values, we can get a criteria that when the number of sensors reaching some significant level is as large as we expect, the amount of acquired recordings is statis-tically enough. Furthermore, both of the expected advantages of Beamformer-based ICA are demonstrated with simulation data. Beamformer-based ICA also works with correlated sources even when MCB fails. From the results of simulation, phantom and real exper-iment data for validation of head motion correction and super resolution, we can correct the inaccurate source localization caused by head motion and get more accurate source localization result by combining the different head poses using SLIM.

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