Analysis of complex-valued functional magnetic resonance imaging data: are we just going through a "phase"?

Functional magnetic resonance imaging (fMRI) data are acquired as a natively complex data set, however for various reasons the phase data is typically discarded. Over the past few years, interest in incorporating the phase information into the analyses has been growing and new methods for modeling and processing the data have been developed. In this paper, we provide an overview of approaches to understand the complex nature of fMRI data and to work with the utilizing the full information, both the magnitude and the phase. We discuss the challenges inherent in trying to utilize the phase data, and provide a selective review with emphasis on work in our group for developing biophysical models, preprocessing methods, and statistical analysis of the fully-complex data. Of special emphasis are the use of data-driven approaches, which are particularly useful as they enable us to identify interesting patterns in the complex-valued data without making strong assumptions about how these changes evolve over time, something which is challenging for magnitude data and even more so for the complex data. Finally, we provide our view of the current state of the art in this area and make suggestions for what is needed to make efficient use of the fully-complex fMRI data.