A new high order tensor decomposition: Application to reorientation.

To model the diffusion process in diffusion weighted MRI (DW-MRI), 2^nd order symmetric positive definite (SPD) tensors have been commonly used. SPD tensor models have known limitations, for instance when there are several fiber bundles within a voxel. More elaborate models have thus been devised. In particular, higher order (HO) SPD tensors enable to account for complex diffusivity functions. Applying a spatial transformation to such tensor fields requires an appropriate reorientation strategy to preserve the consistency of the orientation information related to fiber organization. This key step in most DW-MRI related applications remains largely an open question for HO tensors. In this paper, we present a new HO tensor decomposition, which is naturally suited for reorientation. In the proposed representation, the HO tensor is represented as a set of 2^nd order SPD tensors reflecting the underlying fiber bundles. Reorientation results are presented and compared with existing methods on 4^th order tensors.