The inversion of the X-ray Transform on a Compact Symmetric Space

2006/09/12 by Sigurdur Helgason, Sigurđur Helgason, Helgason, Sigurdur
Chemistry · Mathematics · Medicine · #Advanced Algebra and Geometry #Advanced NMR Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Medical Imaging Techniques and Applications #Representation Theory (math.RT) #math.DG #math.RT

paper · pdf · doi:10.48550/arxiv.math/0609336

11 pages

openalex publication_date 2006/09/12 · arxiv created 2006/12/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The X-ray transform on a compact symmetric space M is here inverted by means of an explicit inversion formula. The proof uses the conjugacy of the minimal closed geodesics in M and of the maximally curved totally geodesic spheres in M, proved in Math. Ann. 165 (1966), 309--317.

Related

• Functional relations, sharp mapping properties and regularization of the X-ray transform on disks of constant curvature
• Numerical implementation of geodesic X-ray transforms and their\n inversion
• Inversion of the attenuated geodesic X-ray transform over functions and vector fields on simple surfaces
• Inverting the local geodesic X-ray transform on tensors
• The tensorial X-ray transform on asymptotically conic spaces