  Delineating the associations between images and a vector of covariates is of
central interest in medical imaging studies. To tackle this problem of image
response regression, we propose a novel nonparametric approach in the framework
of spatially varying coefficient models, where the spatially varying functions
are estimated through deep neural networks. Compared to existing solutions, the
proposed method explicitly accounts for spatial smoothness and subject
heterogeneity, has straightforward interpretations, and is highly flexible and
accurate in capturing complex association patterns. A key idea in our approach
is to treat the image voxels as the effective samples, which not only
alleviates the limited sample size issue that haunts the majority of medical
imaging studies, but also leads to more robust and reproducible results.
Focusing on a broad family of piecewise smooth functions, we establish the
estimation and selection consistency, and derive the asymptotic error bounds.
We demonstrate the efficacy of the method through intensive simulations, and
further illustrate its advantages with analyses of two functional magnetic
resonance imaging datasets.
