In neuroimaging studies, it becomes increasingly important to study associations between different imaging modalities using image-on-image regression (IIR), which faces challenges in interpretation, statistical inference, and prediction. Our motivating problem is how to predict task-evoked fMRI activity using resting-state fMRI data in the Human Connectome Project (HCP). The main difficulty lies in effectively combining different types of imaging predictors with varying resolutions and spatial domains in IIR. To address these issues, we develop Bayesian Image-on-image Regression via Deep Kernel Learning Gaussian Processes (BIRD-GP) and develop efficient posterior computation methods through Stein variational gradient descent. We demonstrate the advantages of BIRD-GP over state-of-the-art IIR methods using simulations. For HCP data analysis using BIRD-GP, we combine the voxel-wise fALFF maps and region-wise connectivity matrices to predict fMRI contrast maps for language and social recognition tasks. We show that fALFF is less predictive than the connectivity matrix for both tasks, but combining both yields improved results. Angular Gyrus Right emerges as the most predictable region for the language task (75.9% predictable voxels), while Superior Parietal Gyrus Right tops for the social recognition task (48.9% predictable voxels). Additionally, we identify features from the resting-state fMRI data that are important for task fMRI prediction.

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