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Independent component analysis (ICA) has proven quite useful for the analysis of real world datasets such as functional resonance magnetic imaging (fMRI) data, where the underlying nature of the data is hard to model. It is particularly useful for the analysis of fMRI data in its native complex form since very little is known about the nature of phase. Phase information has been discarded in most analyses as it is particularly noisy. In this paper, we show that a complex ICA approach using a flexible nonlinearity that adapts to the source density is the more desirable one for performing ICA of complex fMRI data compared to those that use fixed nonlinearity, especially when noise level is high. By adaptively matching the underlying fMRI density model, the analysis performance can be improved in terms of both the estimation of spatial maps and the task-related time courses, especially for the estimation of phase of the time course. We also define a procedure for analysis and visualization of complex-valued fMRI results, which includes the construction of bivariate t-maps for multiple subjects and a complex-valued ICASSO scheme for evaluating the consistency of ICA algorithms.