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 for analysis and visualization of such imaging data to separate the signal from the noise and 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 nonstationarity in the data. Of particular note are 1) 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 2) the development of an algorithm, based on multitaper methods, for the removal of approximately periodic physiological artifacts arising from cardiac and respiratory sources.