Regularizing the ODF estimate with the Laplace-Beltrami operator in 3D Polarized Light Imaging

3D-Polarized Light Imaging (3D-PLI) is an optical approach that utilizes the birefringence in postmortem organs (brain/ heart) to map their spatial fiber structure at a submillimeter resolution. Recently, Axer et al. proposed a strategy to bridge it to relatively low diffusion MRI spatial resolution by introducing an estimate of the fiber orientation distribution functions (pliODF) from high-resolution 3D-PLI vector data. However, this method introduces angular errors by discretizing the directional histogram (DH), which limits the spherical harmonics (SH) expansion order. In this work, we propose to improve the angular resolution by making use of the Laplace-Beltrami (LB) operator to regularize the SH coefficients which define the fiber ODF at higher orders.