  Background: Magneto- and Electro-encephalography record the electromagnetic
field generated by neural currents with high temporal frequency and good
spatial resolution, and are therefore well suited for source localization in
the time and in the frequency domain. In particular, localization of the
generators of neural oscillations is very important in the study of cognitive
processes in the healthy and in the pathological brain.
  New method: We introduce the use of a Bayesian multi-dipole localization
method in the frequency domain. Given the Fourier Transform of the data at one
or multiple frequencies and/or trials, the algorithm approximates numerically
the posterior distribution with Monte Carlo techniques.
  Results: We use synthetic data to show that the proposed method behaves well
under a wide range of experimental conditions, including low signal-to-noise
ratios and correlated sources. We use dipole clusters to mimic the effect of
extended sources. In addition, we test the algorithm on real MEG data to
confirm its feasibility.
  Comparison with existing method(s): Throughout the whole study, DICS (Dynamic
Imaging of Coherent Sources) is used systematically as a benchmark. The two
methods provide similar general pictures; the posterior distributions of the
Bayesian approach contain much richer information at the price of a higher
computational cost.
  Conclusions: The Bayesian method described in this paper represents a
reliable approach for localization of multiple dipoles in the frequency domain.
