Motivated by recent data analyses in biomedical imaging studies, we consider a class of image-on-scalar regression models for imaging responses and scalar predictors. We propose using flexible multivariate splines over triangulations to handle the irregular domain of the objects of interest on the images, as well as other characteristics of images. The proposed estimators of the coefficient functions are proved to be root-n consistent and asymptotically normal under some regularity conditions. We also provide a consistent and computationally efficient estimator of the covariance function. Asymptotic pointwise confidence intervals and data-driven simultaneous confidence corridors for the coefficient functions are constructed. Our method can simultaneously estimate and make inferences on the coefficient functions while incorporating spatial heterogeneity and spatial correlation. A highly efficient and scalable estimation algorithm is developed. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed method, which is then applied to the spatially normalized positron emission tomography data of the Alzheimer's Disease Neuroimaging Initiative.

翻译：根据生物医学成像研究中最近的数据分析,我们考虑一组成象反应和卡路里预测器的成象-天际回归模型;我们提议在三角式图中采用灵活的多变样样样条,处理图像上有关对象的不规则领域,以及图像的其他特征;拟议的系数函数估计法证明在某些正常条件下是根一致和无干扰的。我们还为共变函数提供一致和计算效率高的测算器。构建了Asymptic 点信任间隔和数据驱动的系数函数同步信任走廊。我们的方法可以同时估计和推断系数函数,同时纳入空间异性和空间相关性;制定了高效和可缩放的估算算法;对蒙特卡洛进行了模拟研究,以审查拟议方法的有限-抽样性表现,然后应用于阿尔茨海默氏病神经成形倡议的空间标准化正数成像数据。