Motivation: dMRI signal at moderate diffusion-weightings \, b² has contributions from intrinsic (microstructural) kurtosis, and from heterogeneity of compartments. Goal (s): To separate all kurtosis sources and provide a complete set of tensor invariants for a most general distribution of non-Gaussian compartments. Approach: We decompose double diffusion encoding (DDE) signal into irreducible spherical tensor components via harmonic analysis on the rotation group manifold, a 3-dimensional sphere S³. Results: We find a complete set of 18 (covariances) + 12 (microscopic-kurtosis) =33 independent rotational invariants at b² level. Impact: We observe for the first time a 4-fold angular modulation of double diffusion encoding signal in the human brain in vivo. This validates the presence of higher-order tensor anisotropies in brain microstructure, which we fully quantify at the b² level.
Coelho et al. (Tue,) studied this question.