On the V-Line Radon Transform and Its Imaging Applications

الملخص EN

Radon transforms defined on smooth curves are well known and extensively studied in the literature.

In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V.

If the classical two-dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V-line Radon transform is the backbone of scattered radiation imaging in two dimensions.

We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure.

These theoretical results allow the reconstruction of two-dimensional images from Compton scattered radiation collected on a one-dimensional collimated camera.

We illustrate the working principles of this imaging modality by presenting numerical simulation results.