We develop a general framework for estimating orientational and microstructural parameters of neurites. By employing a set of rotational invariants, we analytically reveal 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 differs for white and for gray matter. We reveal hidden degeneracies in MRI parameter estimation for neuronal tissue, provide microstructural and orientational maps in the whole brain without constraints or priors, and assess commonly used parameter constraints.
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