New properties of the V-line Radon transform and their imaging applications

Abstract

This paper reports on new aspects of the so-called V-line Radon transforms (RTs) complementing those reported in an earlier work. These new properties are nicely uncovered and described with Cartesian coordinates. In particular, we show that the V-line RT belongs to the class of RTs on curves in the plane which can be mapped onto the standard RT on straight lines and thereby are fully characterizable and invertible. Next, we show that the effect of geometric inversion on the V-line RT is to produce a new RT on a pair of supplementary circular arcs, which provides a new access to image reconstruction in the so-called Norton's modality of Compton scatter tomography, a front runner in the race for alternatives to current emission imaging.