  Diffusion magnetic resonance imaging (dMRI) is an emerging medical technique
used for describing water diffusion in an organic tissue. Typically, rank-2
tensors quantify this diffusion. From this quantification, it is possible to
calculate relevant scalar measures (i.e. fractional anisotropy and mean
diffusivity) employed in clinical diagnosis of neurological diseases.
Nonetheless, 2nd-order tensors fail to represent complex tissue structures like
crossing fibers. To overcome this limitation, several researchers proposed a
diffusion representation with higher order tensors (HOT), specifically 4th and
6th orders. However, the current acquisition protocols of dMRI data allow
images with a spatial resolution between 1 $mm^3$ and 2 $mm^3$. This voxel size
is much smaller than tissue structures. Therefore, several clinical procedures
derived from dMRI may be inaccurate. Interpolation has been used to enhance
resolution of dMRI in a tensorial space. Most interpolation methods are valid
only for rank-2 tensors and a generalization for HOT data is missing. In this
work, we propose a novel stochastic process called Tucker decomposition process
(TDP) for performing HOT data interpolation. Our model is based on the Tucker
decomposition and Gaussian processes as parameters of the TDP. We test the TDP
in 2nd, 4th and 6th rank HOT fields. For rank-2 tensors, we compare against
direct interpolation, log-Euclidean approach and Generalized Wishart processes.
For rank-4 and rank-6 tensors we compare against direct interpolation. Results
obtained show that TDP interpolates accurately the HOT fields and generalizes
to any rank.
