DICS power localization with real valued coefficients

[Michael Wibral]

Dear Listusers,

this post relates back to an older one where the use of DICS to localize power maxima (without the use of a reference time course) was discussed. For this case it was agreed upon - if I remember correctly - to constrain the filters to be real-valued as only this correctly reflects linear, INSTANTAEUOUS mixing from sources to sensors as it should be given for normal volume conduction, frequencies below 1 kHz and sampling in the same range. Real valued filters also allow to reconstruct real-valued source time-courses.

Here's my question now:
Real valued filters (i.e. only +/- values) should result in DICS also showing the well known problems for correlated sources (that are circumvented for everything but exactly correlated/anticorrelated sources when using complex coefficients and a reference signal) as in this case the whole equation is not very different from a simple fourier transform of the corresponding LCMV solution. Is this correct? Does DICS have problems localizing source power for correlated/coherent sources when constraining it to real valued coefficients? And if not, could someone give a hint where the differences would come from?

Many thanks,
Michael


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