  Functional magnetic resonance imaging (fMRI) enables indirect detection of
brain activity changes via the blood-oxygen-level-dependent (BOLD) signal.
Conventional analysis methods mainly rely on the real-valued magnitude of these
signals. In contrast, research suggests that analyzing both real and imaginary
components of the complex-valued fMRI (cv-fMRI) signal provides a more holistic
approach that can increase power to detect neuronal activation. We propose a
fully Bayesian model for brain activity mapping with cv-fMRI data. Our model
accommodates temporal and spatial dynamics. Additionally, we propose a
computationally efficient sampling algorithm, which enhances processing speed
through image partitioning. Our approach is shown to be computationally
efficient via image partitioning and parallel computation while being
competitive with state-of-the-art methods. We support these claims with both
simulated numerical studies and an application to real cv-fMRI data obtained
from a finger-tapping experiment.
