  With the rapid growth of neuroimaging technologies, a great effort has been
dedicated recently to investigate the dynamic changes in brain activity.
Examples include time course calcium imaging and dynamic brain functional
connectivity. In this paper, we propose a novel nonparametric matrix response
regression model to characterize the nonlinear association between 2D image
outcomes and predictors such as time and patient information. Our estimation
procedure can be formulated as a nuclear norm regularization problem, which can
capture the underlying low-rank structure of the dynamic 2D images. We present
a computationally efficient algorithm, derive the asymptotic theory and show
that the method outperforms other existing approaches in simulations. We then
apply the proposed method to a calcium imaging study for estimating the change
of fluorescent intensities of neurons, and an electroencephalography study for
a comparison in the dynamic connectivity covariance matrices between alcoholic
and control individuals. For both studies, the method leads to a substantial
improvement in prediction error.
