Inversion of the conical Radon transform with vertices on a surface of revolution arising in an application of a Compton camera. (19th April 2017)

• Record Type: Journal Article
• Authors: Moon, Sunghwan
• Is Part Of: Inverse problems. Volume 33:Number 6(2017:Jun.)
• Publication Date: 2017-04-19
• Subjects: conical Radon transform -- Compton camera -- SPECT -- inversion formula -- spherical section transform; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa69c9
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: A Compton camera has been introduced for use in single photon emission computed tomography to improve the low efficiency of a conventional gamma camera. In general, a Compton camera brings about the conical Radon transform. Here we consider a conical Radon transform with the vertices on a rotation symmetric set with respect to a coordinate axis. We show that this conical Radon transform can be decomposed into two transforms: the spherical sectional transform and the weighted fan beam transform. After finding inversion formulas for these two transforms, we provide an inversion formula for the conical Radon transform.