Analytic inversion of a conical Radon transform arising in application of Compton cameras on the cylinder

TL;DR

This paper develops analytic methods for inverting a conical Radon transform relevant to Compton camera imaging in SPECT, aiming to improve image resolution and reduce noise by providing explicit reconstruction formulas.

Contribution

It introduces the first analytic inversion formulas for conical Radon transforms with vertices on a cylinder, advancing imaging techniques in medical tomography.

Findings

Derived explicit reconstruction formulas for the conical Radon transform.

Analyzed the V-line transform with vertices on a circle for planar distributions.

Enhanced understanding of inverse problems in Compton camera imaging.

Abstract

Single photon emission computed tomography (SPECT) is a well established clinical tool for functional imaging. A limitation of current SPECT systems is the use of mechanical collimation, where only a small fraction of the emitted photons is actually used for image reconstruction. This results in large noise level and finally in a limited spatial resolution. In order to decrease the noise level and to increase the imaging resolution, Compton cameras have been proposed as an alternative to mechanical collimators. Image reconstruction in SPECT with Compton cameras yields to the problem of recovering a marker distribution from integrals over conical surfaces. Due to this and other applications, such conical Radon transforms recently got significant attention. In the current paper we consider the case where the cones of integration have vertices on a circular cylinder and axis pointing to the symmetry axis of the cylinder. As main results we derive analytic reconstruction methods for the considered transform. We also investigate the V-line transform with vertices on a circle and symmetry axis orthogonal to the circle, which arises in the special case where the absorber distribution is located in a horizontal plane.