  Fiber orientation distributions (FODs) is a popular model to represent the
diffusion MRI (dMRI) data. However, imaging artifacts such as
susceptibility-induced distortion in dMRI can cause signal loss and lead to the
corrupted reconstruction of FODs, which prohibits successful fiber tracking and
connectivity analysis in affected brain regions such as the brain stem.
Generative models, such as the diffusion models, have been successfully applied
in various image restoration tasks. However, their application on FOD images
poses unique challenges since FODs are 4-dimensional data represented by
spherical harmonics (SPHARM) with the 4-th dimension exhibiting order-related
dependency. In this paper, we propose a novel diffusion model for FOD
restoration that can recover the signal loss caused by distortion artifacts. We
use volume-order encoding to enhance the ability of the diffusion model to
generate individual FOD volumes at all SPHARM orders. Moreover, we add
cross-attention features extracted across all SPHARM orders in generating every
individual FOD volume to capture the order-related dependency across FOD
volumes. We also condition the diffusion model with low-distortion FODs
surrounding high-distortion areas to maintain the geometric coherence of the
generated FODs. We trained and tested our model using data from the UK Biobank
(n = 1315). On a test set with ground truth (n = 43), we demonstrate the high
accuracy of the generated FODs in terms of root mean square errors of FOD
volumes and angular errors of FOD peaks. We also apply our method to a test set
with large distortion in the brain stem area (n = 1172) and demonstrate the
efficacy of our method in restoring the FOD integrity and, hence, greatly
improving tractography performance in affected brain regions.
