A Tucker decomposition process for probabilistic modeling of diffusion magnetic resonance imaging
This work addresses a domain-specific problem for medical imaging researchers and clinicians by enabling more accurate interpolation of HOT data in diffusion MRI, though it is incremental as it builds on existing tensor decomposition and Gaussian process methods.
The authors tackled the problem of interpolating higher-order tensor (HOT) data in diffusion MRI, which is limited by current acquisition protocols, by proposing a Tucker decomposition process (TDP) that accurately interpolates HOT fields and generalizes to any rank, outperforming existing methods in tests on rank-2, 4, and 6 tensors.
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.