A discrete Funk transform on the Cubed Sphere
Résumé
Computing accurately Funk transforms from discrete values is crucial in some applications, such as Q-Ball Imaging in medicine. This paper deals with a new discrete Funk transform devoted to such computation, in the case of a hemispherical grid extracted from the Cubed Sphere with step π/(2N). The approach is based on a spectral method applied on a least squares fitting, in the space of even spherical harmonics with degree at most 2N − 2. We prove various properties satisfied by the new transform, including an analogous description of the pseudoinverse. Remarkably, the transform and the pseudoinverse are expected to be stable, despite the least square fitting is not regularized. Numerical results attest to the accuracy and the stability, in particular for synthetic Gaussian signals from Q-Ball Imaging.
Origine : Fichiers produits par l'(les) auteur(s)