  Diffusion magnetic resonance imaging is an imaging technology designed to
probe anatomical architectures of biological samples in an in vivo and
non-invasive manner through measuring water diffusion. The contribution of this
paper is threefold. First it proposes a new method to identify and estimate
multiple diffusion directions within a voxel through a new and identifiable
parametrization of the widely used multi-tensor model. Unlike many existing
methods, this method focuses on the estimation of diffusion directions rather
than the diffusion tensors. Second, this paper proposes a novel direction
smoothing method which greatly improves direction estimation in regions with
crossing fibers. This smoothing method is shown to have excellent theoretical
and empirical properties. Lastly, this paper develops a fiber tracking
algorithm that can handle multiple directions within a voxel. The overall
methodology is illustrated with simulated data and a data set collected for the
study of Alzheimer's disease by the Alzheimer's Disease Neuroimaging Initiative
(ADNI).
