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Diffusion magnetic resonance imaging (dMRI) is an emerging medical techniqueused for describing water diffusion in an organic tissue. Typically, rank-2tensors quantify this diffusion. From this quantification, it is possible tocalculate relevant scalar measures (i.e. fractional anisotropy and meandiffusivity) employed in clinical diagnosis of neurological diseases.Nonetheless, 2nd-order tensors fail to represent complex tissue structures likecrossing fibers. To overcome this limitation, several researchers proposed adiffusion representation with higher order tensors (HOT), specifically 4th and6th orders. However, the current acquisition protocols of dMRI data allowimages with a spatial resolution between 1 $mm^3$ and 2 $mm^3$. This voxel sizeis much smaller than tissue structures. Therefore, several clinical proceduresderived from dMRI may be inaccurate. Interpolation has been used to enhanceresolution of dMRI in a tensorial space. Most interpolation methods are validonly for rank-2 tensors and a generalization for HOT data is missing. In thiswork, we propose a novel stochastic process called Tucker decomposition process(TDP) for performing HOT data interpolation. Our model is based on the Tuckerdecomposition and Gaussian processes as parameters of the TDP. We test the TDPin 2nd, 4th and 6th rank HOT fields. For rank-2 tensors, we compare againstdirect interpolation, log-Euclidean approach and Generalized Wishart processes.For rank-4 and rank-6 tensors we compare against direct interpolation. Resultsobtained show that TDP interpolates accurately the HOT fields and generalizesto any rank.

A Tucker decomposition process for probabilistic modeling of diffusion magnetic resonance imaging