A discrete Funk transform on the Cubed Sphere - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

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.
Fichier principal
Vignette du fichier
Bellet_discreteFunkCubedSphere_20221018.pdf (1.35 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03820075 , version 1 (18-10-2022)
hal-03820075 , version 2 (04-02-2023)

Identifiants

  • HAL Id : hal-03820075 , version 1

Citer

Jean-Baptiste Bellet. A discrete Funk transform on the Cubed Sphere. 2022. ⟨hal-03820075v1⟩
94 Consultations
62 Téléchargements

Partager

Gmail Facebook X LinkedIn More