Image-on-image regression analysis, using images to predict images, is a challenging task, due to (1) the high dimensionality and (2) the complex spatial dependence structures in image predictors and image outcomes. In this work, we propose a novel image-on-image regression model, by extending a spatial Bayesian latent factor model to image data, where low-dimensional latent factors are adopted to make connections between high-dimensional image outcomes and image predictors. We assign Gaussian process priors to the spatially varying regression coefficients in the model, which can well capture the complex spatial dependence among image outcomes as well as that among the image predictors. We perform simulation studies to evaluate the out-of-sample prediction performance of our method compared with linear regression and voxel-wise regression methods for different scenarios. The proposed method achieves better prediction accuracy by effectively accounting for the spatial dependence and efficiently reduces image dimensions with latent factors. We apply the proposed method to analysis of multimodal image data in the Human Connectome Project where we predict task-related contrast maps using subcortical volumetric seed maps.

中文翻译：

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图像对图像回归的空间贝叶斯潜在因子模型

使用图像来预测图像的图像对图像回归分析是一项具有挑战性的任务，因为 (1) 高维和 (2) 图像预测器和图像结果中复杂的空间依赖结构。在这项工作中，我们提出了一种新颖的图像对图像回归模型，通过将空间贝叶斯潜在因子模型扩展到图像数据，其中采用低维潜在因子在高维图像结果和图像预测变量之间建立联系。我们将高斯过程先验分配给模型中空间变化的回归系数，这可以很好地捕捉图像结果之间以及图像预测变量之间的复杂空间依赖性。我们进行了模拟研究，以评估我们方法的样本外预测性能，与不同场景的线性回归和体素回归方法相比。所提出的方法通过有效地考虑空间依赖性并有效地减少具有潜在因素的图像尺寸来实现更好的预测精度。我们将所提出的方法应用于人类连接组项目中的多模态图像数据分析，我们使用皮层下体积种子图预测与任务相关的对比度图。