Analysis of functional magnetic resonance imaging (fMRI) data in its native, complex form has been shown to increase the sensitivity of the analysis both for data driven techniques such as independent component analysis (ICA) and for model-driven techniques; however, the noisy nature of the phase poses a challenge for successful study of fMRI data. In addition, for complex ICA, the inherent scaling ambiguity, which has a phase term, introduces additional difficulty for group analysis and visualization of the results. In this paper, we address these issues, which have been among the main reasons phase information has been traditionally discarded and introduce a phase correction scheme that can be either applied subsequent to ICA of fMRI data or can be incorporated into the ICA algorithm in the form of prior information to eliminate the need for further processing for phase correction. In addition, we introduce methods for visualization of the analysis results as well as preprocessing the complex fMRI data to mitigate the effects of noise in the phase which are not limited to ICA algorithms. We demonstrate the successful application of the methods using actual fMRI data.