  We develop a general analytical and numerical framework for estimating intra-
and extra-neurite water fractions and diffusion coefficients, as well as
neurite orientational dispersion, in each imaging voxel. By employing a set of
rotational invariants and their expansion in the powers of diffusion weighting,
we analytically uncover the nontrivial topology of the parameter estimation
landscape, showing that multiple branches of parameters describe the
measurement almost equally well, with only one of them corresponding to the
biophysical reality. A comprehensive acquisition shows that the branch choice
varies across the brain. Our framework reveals hidden degeneracies in MRI
parameter estimation for neuronal tissue, provides microstructural and
orientational maps in the whole brain without constraints or priors, and
connects modern biophysical modeling with clinical MRI.
