Cumulant tensors from the addition of angular momenta: All diffusion invariants in one abstract

Motivation: The advent of quantitative imaging hinges on revealing the information content of MRI measurements. We provide a complete basis- and hardware-independent “fingerprint" for the diffusion signal up to moderate diffusion-weightings. Goal(s): Find all rotationally invariant information present in the cumulant expansion up to b2. Approach: We classify all invariants of diffusion and covariance tensors in terms of irreducible representations of the group of rotations, discuss their geometric meaning, and relate them to tissue properties. Results: We find a complete set of 21 independent rotational invariants up to b2. Previously studied contrasts are expressed via only 7, while the rest provide novel complementary information. Impact: We map the diffusion covariance tensor onto the addition of angular momenta, and provide all rotational invariants of the cumulant expansion (RICE). RICE apply to >50k publicly available human diffusion MRI datasets, providing new insights into tissue properties.