Estimation of fiber Orientation Probability Density Functions in High Angular Resolution Diffusion Imaging

An estimator of the Orientation Probability Density Function (OPDF) of fiber tracts in the white matter of the brain from High Angular Resolution Diffusion data is presented. Unlike Q-Balls, which use the Funk–Radon transform to estimate the radial projection of the 3D Probability Density Function, the Jacobian of the spherical coordinates is included in the Funk–Radon approximation to the radial integral. Thus, true angular marginalizations are computed, which allows a strict probabilistic interpretation. Extensive experiments with both synthetic and real data show the better capability of our method to characterize complex micro-architectures compared to other related approaches (Q-Balls and Diffusion Orientation Transform), especially for low values of the diffusion weighting parameter.