Towards Resolving Fiber Crossings with Higher Order Tensor Inpainting

The use of second-order tensors for the modeling of data from Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) is limited by their inability to represent more than one dominant direction in cases of crossing fiber bundles or partial voluming. Higher-order tensors have been used in High Angular Resolution Diffusion Imaging (HARDI) to overcome these problems, but their larger number of parameters leads to longer measurement times for data acquisition. In this work, we demonstrate that higher-order tensors that indicate likely fiber directions can be estimated from a small number of diffusion-weighted measurements by taking into account information from local neighborhoods. To this end, we generalize tensor voting, a method from computer vision, to higher-order tensors. We demonstrate that the resulting even-order tensor fields facilitate fiber reconstruction at crossings both in synthetic and in real DW-MRI data, and that the odd-order fields differentiate crossings from junctions.