While most of Radon transform applications to imaging involve integrations over smooth sub-
manifolds of the ambient space, lately important situations have appeared where the …

In this paper, we investigate the relations between the Radon and weighted divergent beam
and cone transforms. Novel inversion formulas are derived for the latter two. The weighted …

In this paper, we address analytically and numerically the inversion of the integral transform
(cone or Compton transform) that maps a function on R^3 to its integrals over conical …

Here we present new L 2 injectivity results for 2D and 3D Compton scattering tomography
(CST) problems in translational geometries. The results are proven through the explicit …

Generalized Radon Transforms and Imaging by Scattered Particles: Radiative Transport
Equation Page 1 Chapter 1 Radiative Transport Equation The radiative transport (or transfer) …

Broken ray transforms (BRTs) are typically considered to be reciprocal, meaning that the
transform is independent of the direction in which a photon travels along a given broken ray …

This paper addresses the cone transform that integrates a function over the surfaces of
circular cones. We derive an inversion formula for the cone transform in n-dimensional …

Here we present a novel microlocal analysis of generalized Radon transforms which
describe the integrals of L^2 functions of compact support over surfaces of revolution of C^∞ …

The paper studies various properties of the V-line transform (VLT) in the plane and the
conical Radon transform (CRT) in. The VLT maps a function to a family of its integrals along …

Even though iterative methods and particularly Maximum Likelihood Expectation-
Maximization (MLEM) algorithms have been established in reconstruction with Compton …