  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.
