A novel coupled transmission-reflection tomography and the V-line Radon transform

Abstract

The Radon transform (RT ) on straight lines deals as mathematical foundation for conventional tomographic imaging (e.g. X-ray scanner, Single Photon Emission Computed Tomography (SPECT), Positron Emission Tomography (PET)) which use only one physical phenomenon, i.e. either transmission or emission of radiation. An imaging concept exploiting jointly two phenomena leads to a Radon transform defined on a geometrical support different from straight lines. In this paper, we propose a new two-dimensional X-ray imaging based on the coupling between transmission and reflection. Its modeling leads to a Radon transform defined on a pair of half-lines forming a vertical letter V, called V-line RT (V -RT ). Moreover we establish the analytic inverse formula of this new transform, which forms the mathematical basis for image reconstruction. Through simulations, image formation and reconstruction results show the feasibility of this new imaging. The main advantage is the use of an one-dimensional detector which does not rotate for two-dimensional image reconstruction.

The Development of Radon Transforms Associated to Compton Scatter Imaging Concepts

“…13. This is why we have called this imaging process transmission-reflection imaging, see [35]. In Fig.…”

“…Original plastic crack (left), V-line Radon transform data (center), Reconstruction (right), reprinted from[35] …”