Single-Shell Return-to-the-Origin Probability Diffusion Mri Measure Under a Non-Stationary Rician Distributed Noise

The Ensemble Average Propagator (EAP) provides a compact theoretical framework to explore the underlying microstructural properties of the tissues with diffusion magnetic resonance imaging. To model tissue characteristics, it is usually required to fit a functional basis to a densely sampled q-space data and then retrieve the EAP-related maps. In this work, we analytically derive a new closed-form formula to calculate one of the EAP features the Return-To-the-Origin Probability (RTOP) map directly from the data leaving aside the EAP estimation step. Our RTOP estimation approach exploits only single-shell data and additionally handles noise-induced bias using a non-stationary log-Rician statistics. We validated our proposal using an in vivo Human Connectome Project database achieving an increased accuracy of the method when subsampling of the q-space was considered and strong correlations to multiple-shell state-of-the-art methods.