  This paper describes a novel nonparametric model for modeling diffusion MRI
signals in q-space. In q-space, diffusion MRI signal is measured for a sequence
of magnetic strengths (b-values) and magnetic gradient directions (b-vectors).
We propose a Poly-RBF model, which employs a bidirectional framework with
polynomial bases to model the signal along the b-value direction and Gaussian
radial bases across the b-vectors. The model can accommodate sparse data on
b-values and moderately dense data on b-vectors. The utility of Poly-RBF is
inspected for two applications: 1) prediction of the dMRI signal, and 2)
harmonization of dMRI data collected under different acquisition protocols with
different scanners. Our results indicate that the proposed Poly-RBF model can
more accurately predict the unmeasured diffusion signal than its competitors
such as the Gaussian process model in {\tt Eddy} of FSL. Applying it to
harmonizing the diffusion signal can significantly improve the reproducibility
of derived white matter microstructure measures.
