Diffusion-weighted magnetic resonance imaging is able to non-invasively visualize the fibrous structure of the human brain white matter. The robust and accurate estimation of the ensemble average diffusion propagator (EAP), based on diffusionsensitized magnetic resonance images, is an important preprocessing step for tractography algorithms or any other derived statistical analysis. In this work, we propose a new regularization strategy for EAP estimation that bridges the gap between modelbased and model-free approaches. The idea is to use a Gaussian prior density which is especially designed for the diffusion signal in the human brain. Therefore, we propose to compute covariance statistics over a family of functions that are typical for human brain white matter. As the considered functions and the physically observed EAPs are usually smooth and local the Gauss-Laguerre basis system is used for realization.