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.

翻译：在神经影像研究中，利用图像对图像回归（IIR）探究不同影像模态间的关联日益重要，但该方法在解释、统计推断和预测方面面临挑战。我们的应用问题源于人类连接组计划（HCP），旨在利用静息态功能磁共振成像（rs-fMRI）数据预测任务诱发fMRI活动。主要难点在于IIR中如何有效整合具有不同分辨率与空间域的多种影像预测因子。为此，我们提出了基于深度核学习高斯过程的贝叶斯图像对图像回归方法（BIRD-GP），并利用斯坦因变分梯度下降法开发了高效的后验计算方法。通过模拟实验，我们证明了BIRD-GP相较于最先进IIR方法的优势。在HCP数据分析中，我们结合体素级fALFF图谱与区域级连接矩阵，预测语言与社交识别任务的fMRI对比图。结果显示，对两类任务而言fALFF的预测能力均弱于连接矩阵，但两者的联合使用可提升预测效果。右角回成为语言任务中最可预测区域（75.9%可预测体素），右顶上小叶则在社交识别任务中表现最优（48.9%可预测体素）。此外，我们还识别出对任务fMRI预测具有重要作用的静息态fMRI特征。