  Modern imaging techniques for probing brain function, including functional
Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging,
and magnetoencephalography, generate large data sets with complex content. In
this paper we develop appropriate techniques of analysis and visualization of
such imaging data, in order to separate the signal from the noise, as well as
to characterize the signal. The techniques developed fall into the general
category of multivariate time series analysis, and in particular we extensively
use the multitaper framework of spectral analysis. We develop specific
protocols for the analysis of fMRI, optical imaging and MEG data, and
illustrate the techniques by applications to real data sets generated by these
imaging modalities. In general, the analysis protocols involve two distinct
stages: `noise' characterization and suppression, and `signal' characterization
and visualization. An important general conclusion of our study is the utility
of a frequency-based representation, with short, moving analysis windows to
account for non-stationarity in the data. Of particular note are (a) the
development of a decomposition technique (`space-frequency singular value
decomposition') that is shown to be a useful means of characterizing the image
data, and (b) the development of an algorithm, based on multitaper methods, for
the removal of approximately periodic physiological artifacts arising from
cardiac and respiratory sources.
