Some analytic properties of the cone transform. (29th January 2019)

• Record Type: Journal Article
• Authors: Terzioglu, Fatma
• Is Part Of: Inverse problems. Volume 35:Number 3(2019)
• Publication Date: 2019-01-29
• Subjects: cone transform -- Compton camera -- Radon transform -- integral geometry -- weighted -- inversion -- microlocal analysis; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aafccf
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This paper addresses the cone transform that integrates a function over the surfaces of circular cones. We derive an inversion formula for the cone transform in n -dimensional Euclidean space for cones having a fixed central axis direction, but having all opening angles and vertices. We also show that the cone transform and its dual are Fourier integral operators, and the normal operator is a pseudo-differential operator. We finally present a differential equation that the cone transform satisfies, which can be seen as a first step in describing the range of the cone transform.