  Diffusion magnetic resonance imaging (dMRI) is a relatively modern technique
used to study tissue microstructure in a non-invasive way. Non-Gaussian
diffusion representation is related to the restricted diffusion and can provide
information about the underlying tissue properties. In this paper, we
analytically derive $n$-th order statistics of the signal considering a
stretched-exponential representation of the diffusion. Then, we retrieve the
Q-space quantitative measures such as the Return-To-the-Origin Probability
(RTOP), Q-space mean square displacement (QMSD), Q-space mean fourth-order
displacement (QMFD). The stretched-exponential representation enables the
handling of the diffusion contributions from a higher $b$-value regime under a
non-Gaussian assumption, which can be useful in diagnosing or prognosis of
neurodegenerative diseases in the early stages. Numerical implementation of the
method is freely available at https://github.com/TPieciak/Stretched.

Signal Processing