Mesh-based spherical deconvolution for physically valid fiber orientation reconstruction from diffusion-weighted MRI

High angular resolution diffusion imaging (HARDI) methods have enabled the reconstruction of complex spin diffusion profiles in central nervous system white matter through diffusion-weighted MRI. For recovery of the underlying fiber orientations, conventional spherical deconvolution techniques based on spherical harmonics typically have difficulty producing fiber orientation distributions (FODs) that simultaneously satisfy the physical constraints of being real, symmetric, and non-negative. In this work, we propose a novel approach for HARDI reconstruction that is guaranteed to generate FODs satisfying these constraints. By using a meshed representation of the unit sphere, we formulate the spherical deconvolution as a convex optimization problem and compute the solution using a projected gradient descent algorithm. Flexible regularization is also included in our method to allow for tuning the sharpness of the reconstructed FOD. In our experiments, we present simulated results to examine the effects of varying the regularization parameters, and we illustrate the robustness of our method by applying it to several biological data sets to reconstruct known white matter fiber geometry.