Diffusion Propagator Estimation Using Gaussians Scattered in q-Space

Abstract

The ensemble average diffusion propagator (EAP) obtained from diffusion MRI (dMRI) data captures important structural properties of the underlying tissue. As such, it is imperative to derive accurate estimate of the EAP from the acquired diffusion data. Taking inspiration from the theory of radial basis functions, we propose a method for estimating the EAP by representing the diffusion signal as a linear combination of 3D anisotropic Gaussian basis functions centered at the sample points in the q-space. This is in contrast to other methods, that always center the Gaussians at the origin in q-space. We also derive analytical expressions for the estimated diffusion orientation distribution function (ODF), the return-to-the-origin probability (RTOP) and the mean-squared-displacement (MSD). We validate our method on data obtained from a physical phantom with known crossing angle and on in-vivo human brain data. The performance is compared with the 3D-SHORE method of [4, 9] and radial basis function based method of [15]. KeywordsDiffusion PropagatorMean Square Displacements (MSD)Diffusion SignalRadial Basis Function MethodNormalized Mean Square Error (NMSE)These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.