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| We are going to use the protocol '''TutorialRaw''' created in the previous tutorial [[Tutorials/TutRawAvg]]. If you have not followed this tutorial yet, please do it now. | We are going to use the protocol '''!TutorialRaw''' created in the previous tutorial [[Tutorials/TutRawAvg|Epoching and Averaging]]. If you have not followed this tutorial yet, please do it now. |
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| Beamfoming methods are | Beamfoming methods scan each targeted voxel/vertex position <<latex($\bf r$)>> and estimate the spatial filter <<latex(${\bf w}_{\bf r,q}$)>>. By multiplying with the MEG recordings <<latex(${\bf m}(t)$)>>, the spatial filter <<latex(${\bf w}_{\bf r,q}$)>> outputs the temporal waveform <<latex($y_{\bf r,q}(t)$)>> of the dipole source at that position with the dipole orientation <<latex($\bf q$)>> as below: |
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| ==== Spatial filter ==== Text |
<<latex(\begin{equation} y_{\bf r,q}(t) = {{\bf w}_{\bf r,q}}^{\rm T}{\bf m}(t)\enspace, \end{equation})>> |
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| ==== Section 2 ==== | where 'T' indicates the transpose of a matrix or vector . ==== Vector-type beamformer ==== For each position <<latex($\mathbf{r}$)>>, three orthogonal spatial filters <<latex($\mathbf{W}_{\mathbf{r}}=\left[\mathbf{w}_{\mathbf{r},\mathbf{q}_x},\mathbf{w}_{\mathbf{r},\mathbf{q}_y},\mathbf{w}_{\mathbf{r},\mathbf{q}_z}\right]$)>> are computed by applying the unit-gain constraint as well as the minimum norm and minimum variance criteria as below: <<latex(\begin{equation} \hat{\mathbf{W}}_{\mathbf r}=(\mathbf{C}_{\rm s}+\alpha\mathbf{I})^{-1}\mathbf{L}_\mathbf{r}\left(\mathbf{L}_\mathbf{r}^{\rm T}(\mathbf{C}_{\rm s}+\alpha\mathbf{I})^{-1}\mathbf{L}_\mathbf{r}\right)^{-1} \enspace, \end{equation})>> where <<latex({\bf C}_{\rm s})>> is the covariance matrix of MEG recordings during window <<latex($T_{\rm_s}$>>, <<latex($\mathbf{I}$)>> is the identity matrix, <<\latex($\mathbf{L}_{\mathbf{r}}$)>> is the gain matrix for the dipole located at position <<latex($\mathbf{r}$)>>, and <<latex(\alpha)>> is the regularization parameter which compromises the minimum norm and minimum variance criteria. ==== Scalar-type beamformer ==== |
Beamforming methods
Authors: Hui-Ling Chan
The estimation of source distribtion is an important step to understand the brain activity from EEG and MEG data. Dipole fitting, minimum norm estimation, and beamformer are three commonly used methods. It has been proved that beamforming methods provide good spatial resolution. This tutorial will show how to apply beamforming methods to MEG data and obtain the statistic map of source activation.
We are going to use the protocol TutorialRaw created in the previous tutorial ?Epoching and Averaging. If you have not followed this tutorial yet, please do it now.
Contents
Introduction
Beamfoming methods scan each targeted voxel/vertex position 
and estimate the spatial filter 
. By multiplying with the MEG recordings 
, the spatial filter outputs the temporal waveform 
of the dipole source at that position with the dipole orientation 
as below:
where 'T' indicates the transpose of a matrix or vector .
Vector-type beamformer
For each position 
, three orthogonal spatial filters ![$\mathbf{W}_{\mathbf{r}}=\left[\mathbf{w}_{\mathbf{r},\mathbf{q}_x},\mathbf{w}_{\mathbf{r},\mathbf{q}_y},\mathbf{w}_{\mathbf{r},\mathbf{q}_z}\right]$](/brainstorm/Tutorials/Beamformers?action=AttachFile&do=get&target=latex_2d3ac467d26334f39241546468515832d42349b6_p1.png "$\mathbf{W}_{\mathbf{r}}=\left[\mathbf{w}_{\mathbf{r},\mathbf{q}_x},\mathbf{w}_{\mathbf{r},\mathbf{q}_y},\mathbf{w}_{\mathbf{r},\mathbf{q}_z}\right]$")
are computed by applying the unit-gain constraint as well as the minimum norm and minimum variance criteria as below:
where
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Transcript written on latex_dd08d32b39252d68c47b686d699fc52aa709af37_p.log.
is the covariance matrix of MEG recordings during window 
is the identity matrix, <<\latex($\mathbf{L}_{\mathbf{r}}$)>> is the gain matrix for the dipole located at position , and latex error! exitcode was 1 (signal 0), transscript follows:
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(see the transcript file for additional information)
Output written on latex_6edeca32a0a729959442a738ed7e7ca04608a046_p.dvi (1 page,
240 bytes).
Transcript written on latex_6edeca32a0a729959442a738ed7e7ca04608a046_p.log.
is the regularization parameter which compromises the minimum norm and minimum variance criteria.
Scalar-type beamformer
Text
Linearly-constrained minimum variance beamformer (LCMV)
Section 1
Text
Section 2
Text
Maximum constrast beamformer (MCB)
Section 1
Text
Section 2
Text
Beamformer-based correlation/coherence imaging
Dynamic imaging of coherent sources (DICS)
Text
Spatiotemporal imaging of linearly-related source components (SILSC)
Text