Our brains usually have markedly different activity during task performance in almost all behavioral domains. It was thought that such individual differences in brain response are attributed to two possible factors, 1) differences in gross brain morphology and 2) different task strategy or cognitive processes. We assume that the individual differences in task-evoked brain activity are, to a great degree, inherent features of individual brain such that can be predicted from task-free measurements at rest. Then, a research question of interest is whether task-free MRI can be used to predict several task-evoked activity maps in multiple behavioral domains.
To answer this question, we propose an image-on-image regression model, which is also a spatial Bayesian latent factor regression model. The task-evoked maps and their spatial correlations are measured through a collection of basis functions. The low-dimensional representation of the basis parameters is obtained by placing a sparse latent factor model. Then we use a scalar-on-image regression model to link the latent factors with task-free maps. Our proposed model is applied to 98 subjects of the Human Connectome Project database.