Smoothing fields of weighted collections with applications to diffusion MRI processing.

Using modern diffusion weighted magnetic resonance imaging protocols, the orientations of multiple neuronal fiber tracts within each voxel can be estimated. Further analysis of these populations, including application of fiber tracking and tract segmentation methods, is often hindered by lack of spatial smoothness of the estimated orientations. For example, a single noisy voxel can cause a fiber tracking method to switch tracts in a simple crossing tract geometry. In this work, a generalized spatial smoothing framework that handles multiple orientations as well as their fractional contributions within each voxel is proposed. The approach estimates an optimal fuzzy correspondence of orientations and fractional contributions between voxels and smooths only between these correspondences. Avoiding a requirement to obtain exact correspondences of orientations reduces smoothing anomalies due to propagation of erroneous correspondences around noisy voxels. Phantom experiments are used to demonstrate both visual and quantitative improvements in postprocessing steps. Improvement over smoothing in the measurement domain is also demonstrated using both phantoms and in vivo human data.