A quantitative analysis of noncircularity for complex-valued fMRI based on semi-blind ICA

The spatial components included in complex-valued functional magnetic resonance imaging (fMRI) data are generally assumed to be noncircular signals. In this paper, we try to quantitatively investigate the noncircularity of fMRI with a measure called the degree of impropriety (DOI). Two semi-blind complex ICA algorithms, the kurtosis maximization (KM) algorithm suitable for separating noncircular sources and the complex fastICA algorithm (CfastICA) derived for recovering circular signals, are performed to estimate the spatial components, and two kinds of fMRI data including a simulated complex-valued fMRI dataset and a real complex-valued fMRI data are used for DOI tests. Results show that, semi-blind KM algorithm always outperforms semi-blind CfastICA algorithm, the DOI indices for the estimated components from the real fMRI data are smaller than those from the simulated fMRI data but significantly larger than typical circular signals. Therefore, it is reasonable to conclude that the complex-valued components of fMRI are noncircular.