In a similar way to that outlined above, we added various source
signals into Gaussian and autoregressive noise. The background noise
parameters (i.e. voxel wise mean and std. deviation in the case of
Gaussian noise and AR parameters in the case of autoregressive noise)
were estimated from the resting state FMRI data. We then added 10
spatial maps and associated time courses taken from ICA decompositions
of various other true FMRI data sets. The sources were chosen to
represent different source processes that commonly are identified in
real FMRI data, e.g. high frequency noise within the ventricular
system, fluctuations in the B 
field homogeneity spatially
located near tissue-air boundraries, activation maps etc. This should
not bias the results of the comparison in favor of PICA given that
these spatial maps originated from different data sets and as such
are not mutually spatially independent. Similarly, the associated time
courses are not uncorrelated. This, we belive, is a more faithful
representation of FMRI data. In FMRI it is often possible (and almost
always advisable) to create experiments under an orthogonal
experimental design which hopefully renders the temporal responses to
external stimulation to be mutually orthogonal. Any additional source
processes, however, can have arbitrary correlation with any column of
the design. We therefore did not impose any constraints on the
associated time courses.