Stochastic maximum likelihood mean and cross-spectrum structure modelling in neuro-magnetic source estimation

In [R.P.P.P. Grasman et al., Frequency domain simultaneous source and source coherence estimation with an application to MEG, IEEE Trans. Biomed. Eng. 51 (1) (2004) 45-55] we proposed to analyze cross-spectrum matrices obtained from electro- or magnetoencephalographic (EEG/MEG) signals, to obtain estimates of the EEG/MEG sources and their coherence. In this paper we extend this method in two ways. First, by modelling such interactions as linear filters, and second, by taking the mean of the signals across different trials into account. To obtain estimates we propose a stochastic maximum likelihood (SML) method, and obtain the concentrated likelihood that includes the trial means.