The inverse problem of multi-channel MEG/EEG data is considered as a parameter estimation
problem. The stability of the solution of the inverse problem, which decreases with
the number of included dipoles, can be improved by either adding constraints to the
model parameters, or by adding more data of related data sets. The latter approach
was taken by Bijma et al. [Bijma F, de Munck JC, Böcker KBE, Huizenga HM, Heethaar
RM. The coupled dipole model: an integrated model for multiple MEG/EEG data sets.
NeuroImage 2004;23(3):890-904; Bijma F, de Munck JC, Huizenga HM, Heethaar RM, Nehorai
A. Simultaneous estimation and testing in multiple MEG data sets. IEEE Trans SP 2005;53(9):3449-60]
by introducing coupling matrices that link dipole parameters and source time functions
of different data sets. Here, the theoretical foundations of the coupled dipole model
are explored and the MUSIC algorithm is generalised to the analysis of multiple related
data sets. Similar to the MUSIC algorithm, the number of sources and the number of
constraints are derived from the data by considering the minimum possible residual
error as a function of the number of sources and constraints. However, contrary to
the MUSIC algorithm, where the minimum residual error can be obtained from an SVD
analysis of a two-way data matrix, here we deal with multiple data sets and therefore
three-way matrix analysis is used. From a simulation study it appears that the number
of sources and constraints can be clearly determined from a generalised SVD analysis.
The generalisation of the MUSIC algorithm to three-way data gives reasonable estimates
of the dipole parameters. These results can be used in the simultaneous analysis of
MEG/EEG data of multiple subjects, multiples data sets of the same subject or models
where subsequent trials of data show habituation effects.