Data-driven analysis methods, in particular independent component analysis (ICA) has proven quite useful for the analysis of functional magnetic imaging (fMRI) data. In addition, by enabling one to work in its native, complex form, complex-valued ICA algorithms provide better estimation performance compared to the traditional approach that uses only the magnitude data. In the complex domain, circularity has been a common assumption even though most data acquisition methods collect fMRI data that end up being noncircular when saved in complex form. In this paper, we show that a complex ICA approach that does not assume circularity and also adapts to the source density is the more desirable one for performing ICA of complex fMRI data. We show that by adaptively matching the underlying fMRI density model, the analysis performance can be improved in terms of both the estimation of the task-related time courses and in the spatial activation.