Symmetric positive semi-definite Cartesian Tensor fiber orientation distributions (CT-FOD)

A novel method for estimating a field of fiber orientation distribution (FOD) based on signal de-convolution from a given set of diffusion weighted magnetic resonance (DW-MR) images is presented. We model the FOD by higher order Cartesian tensor basis using a parametrization that explicitly enforces the positive semi-definite property to the computed FOD. The computed Cartesian tensors, dubbed Cartesian Tensor-FOD (CT-FOD), are symmetric positive semi-definite tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. Next, we show how to use our method for converting higher-order diffusion tensors to CT-FODs, which is an essential task since the maxima of higher-order tensors do not correspond to the underlying fiber orientations. Finally, we propose a diffusion anisotropy index computed directly from CT-FODs using higher order tensor distance measures thus consolidating the whole analysis pipeline of diffusion imaging solely using CT-FODs. We evaluate our method qualitatively and quantitatively using simulated DW-MR images, phantom images, and human brain real dataset. The results conclusively demonstrate the superiority of the proposed technique over several existing multi-fiber reconstruction methods.