  High angular resolution diffusion imaging (HARDI), a type of diffusion
magnetic resonance imaging (dMRI) that measures diffusion signals on a sphere
in q-space, is widely used in data acquisition for human brain structural
connectome analysis. Accurate estimation of the local diffusion, and thus the
structural connectome, typically requires dense sampling in HARDI, resulting in
long acquisition times and logistical challenges. We propose a method to select
an optimal set of q-space directions for recovery of the local diffusion under
a sparsity constraint on the sampling budget. Relevant historical dMRI data is
leveraged to estimate a prior distribution of the local diffusion in a template
space using reduced rank Gaussian process models. For a new subject to be
scanned, the priors are mapped into the subject-specific coordinate and used to
guide an optimized q-space sampling which minimizes the expected integrated
squared error of a diffusion function estimator from sparse samples. The
optimized sampling locations are inferred by an efficient greedy algorithm with
theoretical bounds approximating the global optimum. Simulation studies and a
real data application using the Human Connectome Project data demonstrate that
our proposed method provides substantial advantages over its competitors.
