Existence and uniqueness of the inversion of a generalized Radon transform

Abstract

In this paper, we study a new class of Radon transform defined on circular cones called the conical Radon transform (CRT). There has been a substantial spike of interest towards this integral transform in the last decade mainly due to its connection to the mathematical models of several applications used in different domains such as nuclear industry, homeland security, astrophysics etc. This paper contains new results about the existence and uniqueness of the representation of a function by its CRT with fixed opening angle and fixed axis direction in R3. The results are relevant not only as a new generalized Radon transform but also as a new reconstructing method for imaging systems in applied sciences.