A novel V-line Radon transform and its imaging applications

Conventional tomographies (e.g. X-ray scanner, Positron Emission Tomography), functioning on primary radiation are modeled by the Radon transform (RT) which is an integral transform defined on straight lines. In this paper, we consider a new RT defined on a pair of half-lines forming a letter V, which arises from modeling two-dimensional emission imaging process by Compton scattered gamma rays. We give its definition and establish its analytic inverse to support the feasibility of the reconstruction of a two-dimensional (2D) image from scattered radiation measured on a one-dimensional collimated camera. Moreover, a filtered back-projection inversion method is also constructed. Its main advantages are algorithmic efficiency and computational rapidity. We present numerical simulations to illustrate the working. To sum up, the V-line RT leads not only to a new imaging principle, but also to a new concept of detector with high energetic resolution capable to collect the scattered radiation.