  Functional magnetic resonance imaging (fMRI) plays a crucial role in
neuroimaging, enabling the exploration of brain activity through complex-valued
signals. These signals, composed of magnitude and phase, offer a rich source of
information for understanding brain functions. Traditional fMRI analyses have
largely focused on magnitude information, often overlooking the potential
insights offered by phase data. In this paper, we propose a novel fully
Bayesian model designed for analyzing single-subject complex-valued fMRI
(cv-fMRI) data. Our model, which we refer to as the CV-M&P model, is
distinctive in its comprehensive utilization of both magnitude and phase
information in fMRI signals, allowing for independent prediction of different
types of activation maps. We incorporate Gaussian Markov random fields (GMRFs)
to capture spatial correlations within the data, and employ image partitioning
and parallel computation to enhance computational efficiency. Our model is
rigorously tested through simulation studies, and then applied to a real
dataset from a unilateral finger-tapping experiment. The results demonstrate
the model's effectiveness in accurately identifying brain regions activated in
response to specific tasks, distinguishing between magnitude and phase
activation.
