Beamformer-based ICA

We propose a new method, Beamformer-based ICA, combining ICA with MCB to get higher accuracy source localization. Following the concept of virtual sensors from beam-former, we can combine MCB and 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 in-terest and take them as the ICA input signal. We can obtain some advantages by combining MCB and ICA.

From section 1.1.2, we know that MCB is an efficient and accurate algorithm for source localization. However, the major problems in beamformer are the parameters needed to be well-selected, especially the regularization parameter α. α is a parameter to adjust the tradeoff between specificity and noise sensitivity. The inappropriate value of the regular-ization parameter can result in inaccurate spatial filter estimation. If we want a spatial filter with perfect spatial specificity, that α is 1 and the gain of the filter is 0 at every location expect the target one. This will result in that the norm of the spatial filter is too large and the leakage contributed from all other sources and sensor noise will make the spatial filter very unstable and sensitive to noises. If we take the utility of ICA into consideration, even with some inappropriate α, we can still use ICA to separate leakage from target source.

Although ICA is often used as the approach for noise separation [29, 30], it is a pow-erful method to separate signals into independent components. When we conduct signal analysis with ICA, we often observe temporal activations and the contribution to MEG sensors as topographic mapping of each independent component, when the input data is MEG recordings. From Eq (1.2), the topographic mapping corresponds to the column of W⁻¹. As a result, the resolution of topographic mapping is limited with the input data.

If we want to apply ICA for source localization problem, we must raise the resolution to tomographic mapping instead of using only recordings with limited number of sensors.

Recently a method for ICA component topographic mapping is proposed [31], which is called Electromagnetic Spatiotemporal Independent Component Analysis (EMICA). It de-composes the mixing matrix A into L and B where L is the contribution of the tessellation element on the cortex to sensors, the same as lead field and B specifies the contribution of the source component to the tessellation element on the cortex. Instead of optimizing

A, this algorithm optimizes B as ICA components to reach the purpose of topographic mapping. Because it reconstruct the contribution in the brain cortex, EMICA still gets the result of topographic mapping.

If we take sources filtered from MCB filter, because of the concept of virtual sensors, we can raise the dimension of ICA input signals and accomplish tomographic mapping.

However, there exist a problem that if we take too many filtered signals as the ICA input, it will interfere the optimization in ICA because of too many noises. Using this method, we can use only target source activities as ICA input for reliable and accurate ICA components.

Therefore, we need a threshold to remove the unnecessary noises. We calculate a threshold to extract only target source activities by a simple nonparametric statistical approach [3].

This approach uses maximum statistics [32] to address the multiple comparison problem [33]. It first standardize the empirical distribution of the filtered control recordings and then calculate the maximum T value at each pixel location. Finally, an empirical probability distribution from the maximum T value at each pixel location is obtained. By this empirical probability distribution with some significance level α, the threshold to extract only target source activities is generated.

The critical issue about ICA is the component selection. This is very subjective. Fur-thermore, ICA is sensitive to noise thus tends to incorrect selection of components. ICA component selection depends on temporal activities and topographic distribution. We can-not separate sources outside the brain, in which we are uninterested, according to the tem-poral and topographic information. If we apply MCB first and then ICA, like the algorithm of Beamformer-based ICA, we are able to separate sources outside the brain by using brain region information obtained from MRI. Then applying ICA further can result in indepen-dent brain activities by reducing leakage activities in MCB procedure. That’s the rea-son about the order of applying Maximum Contrast Beamformer (MCB) and Independent Component Analysis (ICA) in the algorithm of Beamformer-based ICA.

Therefore, by combining ICA with MCB, we use ICA to separate sources that fil-tered from MCB spatial filter to get more accurate solution to source localization. Using Beamformer-based ICA, we can ignore some inappropriate adjustment of the regulariza-tion parameter because the leakage is separated by ICA. Moreover, we can raise the ICA resolution of topography distribution in sensor space to the resolution of tomography

dis-tribution in source space using virtual sensor concept of beamformer. The overview of Beamformer-based ICA algorithm is in Figure 2.1.

Figure 2.1: This graph shows the overview of Beamformer-based ICA algorithm.