Analysis of the weighted conical and v-line Radon transform

Abstract

In this article, we investigate the weighted conical Radon transform, a novel class of Radon transforms that takes into account the attenuation effect by integrating a function over circular cones. This transform has significant applications in nuclear tomography imaging, the nuclear industry, and homeland security. We propose new inversion formulas for the weighted conical Radon transform, which an explicit formula and a formula based on convolution frames. Furthermore, we provide numerical simulations designed for 2D situation.