On the concept of scattered gamma-ray imaging and corresponding generalized Radon transforms

Abstract

Abstract. This paper reviews the concept of gamma-ray imaging based on Compton scattered radiation introduced some years ago. We describe its mathematical supporting structure of generalized Radon transforms and point out its main advantages in view of applications in nuclear medicine, industrial non-destructive evaluation, nuclear waste surveillance and fissile materials transportation monitoring. Some possible generalizations are mentioned as future research topics.Résumé. Dans cet article, nous présentons le concept d'imagerie gamma basée sur le rayonnement diffusé par effet Compton, qui aété introduit quelques années auparavant. Nous exposons la structure mathématique des transformations de Radon généralisées sous-jacente et passons en revue ses propriétés avantageuses en vue d' applications en médecine nucléaire, contrôle non-destructif industriel, surveillance des dépôts de déchets radioactifs et contrôle du transport des matériaux fissiles. Quelques généralisations de ce concept sont susceptibles de recherche future.

The Development of Radon Transforms Associated to Compton Scatter Imaging Concepts

“…where H(z) is the Heaviside unit step function. More details can be found in [11], in particular for g(r) ∼ r −2 this kernel has the shape of a "Mexican hat". We now give the expressions of the inverse transforms, which are used in the reconstruction of the unknown density f (x, y, z).…”

“…As the support of f (x, y, z) is in the upper space z > 0, we may extend the ζ integration to the full R. Thus the expression of equation (12), is just a convolution where the unknown function is F l . Hence by standard de-convolution, the Fourier transform of A ζ ν being known, one gets back F l (Q, P ), which is the one dimensional Fourier transform in the last variable Z of F l (Q, Z), leading indirectly to the reconstruction of f (x, y, z) (for details follow [8,11]).…”