Intracerebral dipole sources of EEG FFT power maps

TLDR: The described method opens a way to compute intracerebral source localizations of ongoing EEG activity by constructing a sine-cosine diagram of the Fourier-transformed data, which is the least error compromise landscape of all possible landscapes during the paradigmatic cycle of the given FFT frequency.

Abstract: The described method opens a way to compute intracerebral source localizations of ongoing EEG activity. A sine-cosine diagram of the Fourier-transformed data is constructed for each frequency point, forming a "FFT constellation" of entries. Into the FFT constellation of each diagram, a straight line is fitted which produces the least squared deviation sum between the original entry positions and their orthogonal projections onto that line. The map landscape described by the voltages between the projected positions ("FFT approximation") is the least error compromise landscape of all possible landscapes during the paradigmatic cycle of the given FFT frequency. The map thus constructed can be used in the usual dipole source localization procedures. There is one for each FFT frequency point. The squared forward solution of the fitted dipole source and the squared FFT approximation map are "power maps" which are very similar to the original power map. For an average-reference power map with two peaks, the source tends to lie between the peaks; a power map with one peak might show closely neighboring maximal and minimal potential values in the FFT approximation, indicative of a tangential source close to the surface.