## Robust Magnetic Source Imaging of Brain Activities

### Abstract

To discover brain functionalities, we need to do brain source imaging. Magnetoencephalography (MEG) can record brain signals non-invasively with superior temporal resolution and high Signal-to-Noise Ratio (SNR).

There are some issues about magnetic source imaging, like the amount of MEG recordings, the appropriate approach for signal analysis and source localization and head motion correction. We propose some methods to overcome these difficulties. First, we use statistical hypothesis test to reveal the discrimination between the selected active and baseline states. By revealing their discrimination, we can set an evaluation criterion for the amount of recordings.

Second, in order to conduct signal analysis, Independent Component Analysis (ICA) is an powerful method which can retrieve independent components from the linear mixture of sources, under the assumption that components are statistical independent. However, the resolution of ICA topography distribution is in sensor space and it is necessary to raise the resolution to tomography distribution in source space.

Many algorithms are proposed to solve the problem of source localization. In recent years, the most attracting method is Beamforming. It can obtain the activation magnitude of the targeted source by imposing the unit-gain constraint while suppressing the contribution from other sources by applying the minimum variance criterion. Maximum Contrast Beamformer (MCB) is an outstanding method that it can estimate the orientation of the spatial filter from an analytical form which is generated from maximizing the contrast of active state and control state. However, the major problems in beamformer are the parameters needed to be well-selected, especially the regularization parameter. The inappropriate value of the regularization parameter can result in inaccurate spatial filter estimation.

We get more accurate solution to source localization by combining ICA with MCB, which is called 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 signals. As a result, with inappropriate regularization parameter of beamfermer, we can use ICA to separate leakage from target source. Furthermore, we can raise ICA from topography distribution to tomography distribution by the virtual sensor concept of beamformer.

Third, there are still some factors that will affect the accuracy of source localization, like the head motion during MEG experiments. This is unavoidable during MEG studies with long signal recording time. Many algorithms are proposed to solve this problem. With Stabilized Linear Model (SLIM), we can virtually increase the sensor number of MCB model to reduce the localization error induced from head motion and improve the accuracy of source localization simultaneously.

### Results

Experiments with simulation and real data are used to validate the proposed methods. According to the experiments, by revealing the discrimination between the selected active and baseline states, we can set an evaluation criterion for the amount of recordings. Moreover, as aforementioned, the expected advantages of Beamformer-based ICA are demonstrated with simulation data. Applying SLIM into MCB is also validated that it is able to reduce the localization error induced from head motion and improve the accuracy of source localization by combining the different head poses.

**a. Statistical Evaluation of the Amount of Recordings**

We take the recordings of the left index finger lifting for statistical analysis. We apply paired t-test to selected active and control states of each MEG sensor. In Figure 1, 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 when the number of trials increase, the p-value becomes smaller, which also means more significant.

###### Figure 1 : (a)Synchronously averaging recordings with increasing number of trials, for a period of 30 trials. (b) Selecting the baseline and active states from the raw recordings, without synchronously averaging.

**b. Beamformer-based ICA**

We conduct the simulation data to validate Beamformer-based ICA. The ground truth is as Figure 2. We set two simulated sources with different correlation. The results of Beamformer-based ICA are shown in Table 1. We set the regularization paramter in MCB as 0.003, which is an inappropriate value. Because of inappropriate regularization paramter, the results of MCB are inaccurate. After applying Beamformer-based ICA (BICA), we can separate sources into two components in temporal activation and tomographic distribution when two sources are uncorrelated and partially correlated.

###### Figure 2 : Ground truth of the simulated recordings for Beamformer-based ICA.

correlation | uncorrelated | partially correlated |

MCB | ||

BICA |

###### Table 1 : Beamformer-based ICA when the regularization parameter is 0.003. The top row is the results of MCB when the regularization parameter is 0.003. The bottom row is the results of Beamformer-based ICA with the same value of regularization parameter.

**c. Head Motion Correction**

We take the recordings of gender discrimination for validation. we select the time with 139 ms in temporal area for objects recognition. After applying SLIM to MCB, both temporal and occipital activation appeared in the F-statistical map.

Lean Backward | Lean Forward | SLIM | |

103ms |