  A novel approach is presented for group statistical analysis of diffusion
weighted MRI datasets through voxelwise Orientation Distribution Functions
(ODF). Recent advances in MRI acquisition make it possible to use high quality
diffusion weighted protocols (multi-shell, large number of gradient directions)
for routine in vivo study of white matter architecture. The dimensionality of
these data sets is however often reduced to simplify statistical analysis.
While these approaches may detect large group differences, they do not fully
capitalize on all acquired image volumes. Incorporation of all available
diffusion information in the analysis however risks biasing the outcome by
outliers. Here we propose a statistical analysis method operating on the ODF,
either the diffusion ODF or fiber ODF. To avoid outlier bias and reliably
detect voxelwise group differences and correlations with demographic or
behavioral variables, we apply the Low-Rank plus Sparse (L + S) matrix
decomposition on the voxelwise ODFs which separates the sparse individual
variability in the sparse matrix S whilst recovering the essential ODF features
in the low-rank matrix L. We demonstrate the performance of this ODF L + S
approach by replicating the established negative association between global
white matter integrity and physical obesity in the Human Connectome dataset.
The volume of positive findings agrees with and expands on the volume found by
TBSS, Connectivity based fixel enhancement and Connectometry. In the same
dataset we further localize the correlations of brain structure with
neurocognitive measures such as fluid intelligence and episodic memory. The
presented ODF L + S approach will aid in the full utilization of all acquired
diffusion weightings leading to the detection of smaller group differences in
clinically relevant settings as well as in neuroscience applications.
