Injectivity of Rotation invariant windowed Radon transforms.

Abstract : We consider rotation invariant windowed Radon transforms that integrate a function over hyperplanes by using a radial weight (called window). T. Quinto proved their injectivity for square integrable functions of compact support. This cannot be extended in general. Actually, when the Laplace transform of the window has a zero with positive real part , the windowed Radon transform is not injective on functions with a Gaussian decay at infinity, depending on . Nevertheless, we give conditions on the window that imply injectivity of the windowed Radon transform on functions with a more rapid decay than any Gaussian function.
Type de document :
Article dans une revue
Journal of Mathematical Analysis and applications, Elsevier, 2006, 316 (2), pp.383--396
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00271785
Contributeur : Hermine Biermé <>
Soumis le : jeudi 10 avril 2008 - 12:02:54
Dernière modification le : mercredi 12 octobre 2016 - 01:16:59

Identifiants

  • HAL Id : hal-00271785, version 1

Collections

Citation

Hermine Biermé. Injectivity of Rotation invariant windowed Radon transforms.. Journal of Mathematical Analysis and applications, Elsevier, 2006, 316 (2), pp.383--396. <hal-00271785>

Partager

Métriques

Consultations de la notice

80