Learning Low-Rank Tensor Approximation for {GPU}-based Tractography

Fast algorithms for diffusion MRI tractography are required due to the increasing amounts of diffusion MRI data, and the increasing popularity of whole-brain tractography. Representing fiber orientation density functions (fODFs) as higher-order tensors and extracting main fiber directions from them via low-rank tensor approximation is a state-of-the-art variant of streamline tractography, but involves a computationally costly nonlinear optimization in each integration step. In this work, we demonstrate that unsupervised training of a neural network to map fODF coefficients to the corresponding fiber contributions directly is not only faster, but also achieves lower approximation residuals. This is due to the fact that training the network amounts to a joint optimization of all fiber contributions, while traditional algorithms follow an alternating optimization strategy. However, we observe that the traditional approach implicitly favors sparse solutions, and that a corresponding explicit regularization is required to obtain useful results with a joint optimization strategy. Building on those insights, we create the first GPU-based implementation of low-rank tractography, which achieves a speedup by a factor of 68, compared to traditional tractography on a single CPU core, while at the same time improving the median dice.