Estimating Spatially-Smoothed Fiber Orientation Distribution from Diffusion-MRI Experiments

Diffusion-weighted magnetic resonance imaging (D-MRI) is a noninvasive in vivo technique for probing the microstructural architecture of biological tissues. At each voxel, the fiber orientation distribution (FOD) characterizes local fiber configurations and orientations and is therefore a central object of estimation in D-MRI analysis. We propose the Nearest-Neighbor Adaptive Regression Model (NARM), a spatially adaptive framework for FOD estimation that performs weighted local likelihood estimation over nested spatial neighborhoods, where the weights jointly encode spatial proximity and similarity among neighboring FODs, measured by either the optimal transport or Hellinger distance. To prevent over-smoothing while preserving structural heterogeneity, we introduce a voxel-wise rescaling scheme and a data-driven stopping rule based on minimum nearest-neighbor dissimilarity. We further develop a configuration-aware strategy for selecting the similarity-smoothing parameter, allowing the smoothing strength to adapt to local fiber complexity. Simulation studies demonstrate that NARM improves FOD estimation accuracy relative to voxel-wise methods and the existing spatial smoothing approach PMARM. Application to test-retest data from the Human Connectome Project additionally shows that NARM yields more reproducible FOD estimates. Implementation details and scripts for the simulation and real data analyses are available at https://github.com/jie108/NARM