SVD Technique Applied in a 3D Inverse Imaging Problem

Abstract

We study the validity of the numerical implementation of the direct Conical Radon Transform, the so called TC. This operator is at the core of imaging based on Compton scattered radiation emitted by a medical object which has received an injection of radiotracer. The TC is basically an integral transformation over conical surfaces of fixed axis, and it models the data acquisition step in an ideal frame. The inversion of the TC by singular value decomposition SVD is shown to be satisfactory on a 3D Shepp-Logan brain phantom, confirming that the numerical implementation of the direct model is adequate.
It also provides useful information related to the discretization of the direct problem. Finally, we analyze the applicability of the SVD technique for Compton imaging reconstruction in this 3D context.