M.S.: Symmetric positive-definite Cartesian tensor orientation distribution functions

• We propose a novel method to estimate a field of orientation distribution functions (ODF) from a given set of diffusion weighted magnetic resonance (DT-MR) images. • We use Higher Order Symmetric Positive Definite Cartesian Tensors to model ODF profiles. • Our model explicitly enforces the positive definite property to the computed ODFs. • The computed Cartesian tensors, dubbed Cartesian Tensor-ODF (CT-ODF), are symmetric positive definite tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. • Furthermore, we show how to use our method for converting higher-order diffusion tensors to CT-ODFs. This is an essential task since the maxima of higher-order tensors do not correspond to the underlying fiber orientations. • The DT-MR signal for a given magnetic gradient direction g and gradient weighting b can be modeled using the standard multi-fiber reconstruction framework as: where w is a weighting non-negative spherical function and B is basis function. • We approximate w using higher order Cartesian tenso