Inversion of a New V-line Radon Transform and its Numerical Analysis

Abstract

A new Radon transform defined on a discontinuous curve formed by a pair of half-lines forming a letter V is defined and studied. We establish its analytic inverse formula, its related filtered back-projection reconstruction procedure and its numerical analysis. These theoretical results allow the reconstruction of two-dimensional images of a radiating object from its Compton scattered rays measured on a one-dimensional collimated camera. Numerical simulations results illustrate the performance of the new imaging process.

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

“…This transform is a member of the family of the socalled T V -transform ( [4], [5], [6], [7], [8]). The simple T Vtransform was first proposed by Basko [9] in 1997 as a model for image formation in a two-dimensional Compton camera.…”

“…The Vline Radon transform is also considered as a two-dimensional version of the Conical Radon Transform (CRT ) which have been introduced some years ago ( [5], [10], [11], [12], [13]). These generalized Radon transforms (T V and CRT ) have numerous applications in imaging science, in particular in new Compton scattering emission imaging ( [4], [5], [6], [7], [8], [10], [11], [12], [13]). …”