Linear transforms for Fourier data on the sphere: application to high angular resolution diffusion MRI of the brain.

ABSTRACT: This paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2-sphere in three-dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk-Radon Transform (FRT), which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data. The new family of transforms is characterized theoretically, and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics. After these general discussions, attention is focused on a particular new transform from this family that we name the Funk-Radon and Cosine Transform (FRACT). Based o

SUBMITTER: Haldar JP 

PROVIDER: S-EPMC3594568 | biostudies-literature | 2013 May

REPOSITORIES: biostudies-literature