Regularized, fast, and robust analytical Q‐ball imaging

We propose a regularized, fast, and robust analytical solution for the Q-ball imaging (QBI) reconstruction of the orientation distribution function (ODF) together with its detailed validation and a discussion on its benefits over the state-of-the-art. Our analytical solution is achieved by modeling the raw high angular resolution diffusion imaging signal with a spherical harmonic basis that incorporates a regularization term based on the Laplace-Beltrami operator defined on the unit sphere. This leads to an elegant mathematical simplification of the Funk-Radon transform which approximates the ODF. We prove a new corollary of the Funk-Hecke theorem to obtain this simplification. Then, we show that the…

• MU
  McGill University
• MF
  Max-Planck-Institut für Kognitions- und Neurowissenschaften